1 If point C is at -9 and point D is at 7, find a point E on CD¯¯¯¯¯¯¯¯
such that the ratio of CE¯¯¯¯¯¯¯¯ to CD¯¯¯¯¯¯¯¯ is 34
(1 point)
A-7
B 3
C 5
D12
2 Using the numberline, which segment is congruent to
A KL
B LN
C JM
D GO
3 Using the number line above, what is the midpoint of MG¯¯¯¯¯¯¯¯¯
?(1 point)
A J
B I
C L
D O
4 What is the perimeter of a rectangle with a width of 11 inches and a length of 14 inches?(1 point)
5 What is the area of a triangle with a base of 20 inches and a height of 12 inches?(1 point)
6 What is the area of a circle with a radius of 7 inches. round to the nearest tenth. (1 point)
7 The midpoint of UV
is (4,3). The coordinates of one endpoint are U (11, -2). Find the coordinates of the other endpoint, V. (1 point)
8 Given the points below, find the distance from X to Y. Round to the nearest hundredth.
X(-9,2) and Y(5, -4)
1. To find the point E on CD¯¯¯¯¯¯¯¯ such that the ratio of CE¯¯¯¯¯¯¯¯ to CD¯¯¯¯¯¯¯¯ is 34, we can set up a proportion. Since the ratio of CE to CD is 34, we can write:
CE/CD = 34/100 (since 34 is the numerator and CD is the denominator)
To find CE, we can set up the equation:
CE = (34/100) * CD
Given that point C is at -9 and point D is at 7, the length of CD is:
CD = 7 - (-9) = 7 + 9 = 16
Substituting this value into the equation, we get:
CE = (34/100) * 16 = 5.44
Therefore, the point E on CD¯¯¯¯¯¯¯¯ such that the ratio of CE¯¯¯¯¯¯¯¯ to CD¯¯¯¯¯¯¯¯ is 34 is approximately 5.44. Since this is not one of the given answer choices, none of the options are correct.
2. To determine which segment on the number line is congruent to KL, we need to find the segment that has the same length as KL. Since the lengths of the segments are not provided, it is not possible to determine which segment is congruent to KL based on the given information.
3. To find the midpoint of MG¯¯¯¯¯¯¯¯¯, we can use the midpoint formula. The coordinates of point M are (5, 1) and the coordinates of point G are (-5, 5). The midpoint formula states that the x-coordinate of the midpoint is the average of the x-coordinates of the endpoints and the y-coordinate of the midpoint is the average of the y-coordinates of the endpoints.
For the x-coordinate of the midpoint: (5 + (-5)) / 2 = 0/2 = 0
For the y-coordinate of the midpoint: (1 + 5) / 2 = 6/2 = 3
Therefore, the midpoint of MG¯¯¯¯¯¯¯¯¯ is (0, 3). The correct answer is B: I.
4. The perimeter of a rectangle is given by the formula P = 2w + 2l, where w is the width and l is the length. Given that the width is 11 inches and the length is 14 inches, we can substitute these values into the equation:
P = 2(11) + 2(14) = 22 + 28 = 50
Therefore, the perimeter of the rectangle is 50 inches.
5. The area of a triangle is given by the formula A = (1/2)bh, where b is the base and h is the height. Given that the base is 20 inches and the height is 12 inches, we can substitute these values into the equation:
A = (1/2)(20)(12) = 120
Therefore, the area of the triangle is 120 square inches.
6. The area of a circle is given by the formula A = πr^2, where r is the radius. Given that the radius is 7 inches, we can substitute this value into the equation:
A = π(7)^2 ≈ 153.94
Therefore, the area of the circle is approximately 153.94 square inches.
7. The midpoint of UV is given as (4,3), and the coordinates of one endpoint are U(11, -2). To find the coordinates of the other endpoint V, we can use the midpoint formula. The midpoint formula states that the x-coordinate of the midpoint is the average of the x-coordinates of the endpoints, and the y-coordinate of the midpoint is the average of the y-coordinates of the endpoints.
For the x-coordinate of the other endpoint V: 2 * 4 = 8, and 8 - 11 = -3
For the y-coordinate of the other endpoint V: 2 * 3 = 6, and 6 - (-2) = 8
Therefore, the coordinates of the other endpoint V are (-3, 8).
8. To find the distance from X(-9,2) to Y(5, -4), we can use the distance formula. The distance formula states that the distance between two points (x1, y1) and (x2, y2) is given by:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Substituting the coordinates into the formula, we get:
d = sqrt((5 - (-9))^2 + (-4 - 2)^2) = sqrt((14)^2 + (-6)^2) = sqrt(196 + 36) = sqrt(232) ≈ 15.23
Therefore, the distance from X to Y is approximately 15.23.
1. To find point E, we need to find the coordinates that satisfy the given ratio. The ratio of CE to CD is given as 34.
Let's calculate the distance between points C and D first:
CD = D - C = 7 - (-9) = 16
Next, we need to find the coordinate that divides CD into the ratio of 34:16.
CE/CD = 34/16 = 17/8
Let's assume the coordinate of point E is x. Since E is on the line segment CD, we can set up the following equation:
CE/CD = (x - (-9))/16 = 17/8
Cross-multiplying, we get:
8(x + 9) = 17 * 16
Simplifying the equation:
8x + 72 = 272
Subtracting 72 from both sides:
8x = 200
Dividing both sides by 8:
x = 25
Therefore, the coordinate of point E is 25.
The answer is A-7.
2. To determine which segment is congruent to KL, we need to compare the distances between the different segments:
KL is the segment between points K and L.
LN is the segment between points L and N.
JM is the segment between points J and M.
GO is the segment between points G and O.
From the given choices, the segment congruent to KL is LN.
The answer is B LN.
3. To find the midpoint of MG, we need to calculate the average of the coordinates of points M and G.
The coordinate of point M is -1.
The coordinate of point G is 5.
To find the midpoint, we add the x-coordinates and divide by 2, and do the same for the y-coordinates:
Midpoint(x, y) = ((-1 + 5) / 2, (12 + 8) / 2)
Simplifying:
Midpoint(x, y) = (4/2, 20/2)
Midpoint(x, y) = (2, 10)
Therefore, the midpoint of MG is (2, 10).
The answer is B I.
4. The perimeter of a rectangle is the sum of all four sides.
Given:
Width = 11 inches
Length = 14 inches
The formula to calculate the perimeter of a rectangle is:
Perimeter = 2 * (Length + Width)
Substituting the given values:
Perimeter = 2 * (14 + 11)
Perimeter = 2 * 25
Perimeter = 50 inches
Therefore, the perimeter of the rectangle is 50 inches.
The answer is 50.
5. The formula to calculate the area of a triangle is:
Area = (Base * Height) / 2
Given:
Base = 20 inches
Height = 12 inches
Substituting the given values:
Area = (20 * 12) / 2
Area = 240 / 2
Area = 120 square inches
Therefore, the area of the triangle is 120 square inches.
The answer is 120.
6. The formula to calculate the area of a circle is:
Area = π * (Radius)^2
Given:
Radius = 7 inches
Substituting the given value:
Area = π * (7)^2
Area = π * 49
Area ≈ 153.94 square inches (rounded to the nearest tenth)
Therefore, the area of the circle is approximately 153.94 square inches.
The answer is approximately 153.94.
7. The midpoint of UV is given as (4,3), and one endpoint U is given as (11, -2).
To find the coordinates of the other endpoint V, we can calculate the distance between the midpoint and U and then extend the same distance in the opposite direction from the midpoint.
The distance between U and the midpoint (4,3) in terms of the x-coordinate is:
4 = (11 + x) / 2
Simplifying the equation:
8 = 11 + x
x = 8 - 11
x = -3
The x-coordinate of the other endpoint V is -3.
To find the y-coordinate of V, we subtract the y-coordinate of the midpoint from the y-coordinate of U:
3 = -2 + y
y = 3 + 2
y = 5
Therefore, the coordinates of the other endpoint V are (-3, 5).
The answer is (-3, 5).
8. To find the distance between points X and Y, we can use the distance formula:
Distance = √((X2 - X1)^2 + (Y2 - Y1)^2)
Given:
X1 = -9, Y1 = 2 (coordinates of point X)
X2 = 5, Y2 = -4 (coordinates of point Y)
Substituting the given values:
Distance = √((5 - (-9))^2 + (-4 - 2)^2)
Distance = √((5 + 9)^2 + (-4 - 2)^2)
Distance = √((14)^2 + (-6)^2)
Distance = √(196 + 36)
Distance = √232
Distance ≈ 15.23 (rounded to the nearest hundredth)
Therefore, the distance from X to Y is approximately 15.23.
The answer is approximately 15.23.
1. To find the point E, we need to divide the segment CD into two parts, CE and ED, such that the ratio of CE to CD is 34.
First, calculate the length of CD by subtracting the x-coordinate of point C from the x-coordinate of point D: CD = 7 - (-9) = 16.
Next, calculate the length of CE by multiplying the length of CD by the ratio 34/35: CE = CD * (34/35) = 16 * (34/35) = 16 * 0.9714 ≈ 15.54.
So, the x-coordinate of point E will be the x-coordinate of point C plus the length of CE, which is -9 + 15.54 ≈ 6.54.
Therefore, the point E on CD such that the ratio of CE to CD is 34 is approximately (6.54, y), where y can be any value within the range of the y-coordinates of points C and D.
Answer: B) 3
2. To determine which segment is congruent to KL, we need to compare the lengths of the segments using the numberline.
Given that A is at -2, K is at -4, L is at -1, and N is at 0, we can determine the lengths of the segments:
Segment KL: |-1 - (-4)| = |3| = 3
Segment LN: |0 - (-1)| = |1| = 1
Segment JM: |3 - (-2)| = |5| = 5
Segment GO: This segment is not specified in the question.
Comparing the lengths, we find that segment KL has a length of 3.
Therefore, segment KL is congruent to itself.
Answer: A) KL
3. To find the midpoint of MG, we need to calculate the average of the x-coordinates and the average of the y-coordinates of the points M and G.
Given that M is at -2 and G is at 6 on the numberline, we can calculate the midpoint:
Midpoint x-coordinate: (-2 + 6)/2 = 4/2 = 2
Midpoint y-coordinate: (1 + 2)/2 = 3/2 = 1.5
Therefore, the midpoint of MG is (2, 1.5).
Answer: B) I
4. The perimeter of a rectangle is calculated by adding up all the sides.
Given that the width is 11 inches and the length is 14 inches:
Perimeter = 2 * (Length + Width)
Perimeter = 2 * (14 + 11)
Perimeter = 2 * 25
Perimeter = 50
Therefore, the perimeter of the rectangle is 50 inches.
Answer: 50 inches
5. The area of a triangle is calculated using the formula: Area = (base * height)/2.
Given that the base is 20 inches and the height is 12 inches:
Area = (20 * 12)/2
Area = 240/2
Area = 120 square inches
Therefore, the area of the triangle is 120 square inches.
Answer: 120 square inches
6. The area of a circle is calculated using the formula: Area = Pi * (radius)^2, where Pi is a constant approximately equal to 3.14159.
Given that the radius is 7 inches:
Area = 3.14159 * (7)^2
Area = 3.14159 * 49
Area ≈ 153.938 square inches
Therefore, the area of the circle is approximately 153.938 square inches.
Answer: Approximately 153.938 square inches
7. The midpoint of a line segment is the average of the coordinates of the endpoints.
Given that the midpoint is (4, 3) and one endpoint is U (11, -2), we can find the coordinate of the other endpoint, V.
V's x-coordinate = 2 * midpoint x-coordinate - U's x-coordinate
V's y-coordinate = 2 * midpoint y-coordinate - U's y-coordinate
V's x-coordinate = 2 * 4 - 11 = 8 - 11 = -3
V's y-coordinate = 2 * 3 - (-2) = 6 + 2 = 8
Therefore, the coordinates of the other endpoint, V, are (-3, 8).
Answer: (-3, 8)
8. To find the distance between two points, we use the distance formula:
Distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Given that X is at (-9, 2) and Y is at (5, -4), we can calculate the distance:
Distance = sqrt((5 - (-9))^2 + (-4 - 2)^2)
Distance = sqrt((5 + 9)^2 + (-4 - 2)^2)
Distance = sqrt(14^2 + (-6)^2)
Distance = sqrt(196 + 36)
Distance = sqrt(232)
Distance ≈ 15.23
Therefore, the distance from X to Y is approximately 15.23.
Answer: Approximately 15.23.