Find the midpoint of AB¯¯¯¯¯¯¯¯
if A(-3,8) and B(-7,- 6).
To find the midpoint of a line segment on a coordinate plane, we use the midpoint formula:
Midpoint = ( (x1 + x2)/2, (y1 + y2)/2)
In this case, A has coordinates (-3,8) and B has coordinates (-7,-6).
The x-coordinate of the midpoint is (x1 + x2)/2 = (-3 + -7)/2 = -10/2 = -5.
The y-coordinate of the midpoint is (y1 + y2)/2 = (8 + -6)/2 = 2/2 = 1.
Therefore, the midpoint of AB is (-5,1).
The figure below shows circle O inscribed inside square ABCD. Find the area of the shaded region to the nearest tenth.
18
Unfortunately, without a visual representation of the described figure, it is impossible to determine the area or shaded region accurately. Can you please provide more information or a visual representation of the figure?
In the figure below, square ABCD is inscribed in circle O. if the perimeter of ABCD is 18, what is area of shaded region?
Since square ABCD is inscribed in circle O, the diagonal of the square is also the diameter of the circle. Let's denote the side length of the square as s.
Since the perimeter of the square is 18, we have s + s + s + s = 18, which simplifies to 4s = 18. Dividing both sides by 4, we find s = 4.5.
The diagonal of the square can be found using the Pythagorean theorem. Let's denote the diagonal as d. We have d^2 = s^2 + s^2, which simplifies to d^2 = 2s^2. Substituting the value of s, we get d^2 = 2(4.5^2), which further simplifies to d^2 = 2(20.25) = 40.5. Taking the square root of both sides, we find d ≈ 6.36.
The area of the shaded region is the difference between the area of the circle and the area of the square. The area of the circle is given by A = πr^2, where r is the radius of the circle. Since the radius is half the diameter, the radius is approximately r ≈ 3.18. Therefore, the area of the circle is A = π(3.18)^2 ≈ 31.8.
The area of the square is given by A = s^2, so the area of the square is A = (4.5)^2 = 20.25.
The area of the shaded region is the difference between the area of the circle and the area of the square: 31.8 - 20.25 = 11.55.
Therefore, the area of the shaded region is approximately 11.55 square units.
The midpoint of CD¯¯¯¯¯¯¯¯
is E (2, -1). One endpoint is C (-9,4). What are the coordinates of the other endpoint?
To find the coordinates of the other endpoint, we can use the midpoint formula:
Midpoint = ( (x1 + x2)/2, (y1 + y2)/2)
In this case, the midpoint E has coordinates (2, -1) and one endpoint C has coordinates (-9,4).
Let's denote the coordinates of the other endpoint as (x,y). Plugging the given information into the midpoint formula, we have:
(2, -1) = ( (-9 + x)/2, (4 + y)/2 )
Simplifying, we get:
2 = (-9 + x)/2
-1 = (4 + y)/2
Multiplying both equations by 2 to eliminate the fractions, we have:
4 = -9 + x
-2 = 4 + y
Solving the first equation for x, we get:
x = 4 + 9 = 13
Solving the second equation for y, we get:
y = -2 - 4 = -6
Therefore, the coordinates of the other endpoint are (13, -6).
Find the distance between the points (-8, -2) and (6, -1). Round to the nearest tenth
To find the distance between two points in a coordinate plane, we can use the distance formula:
Distance = √((x2 - x1)^2 + (y2 - y1)^2)
In this case, the two points are (-8, -2) and (6, -1).
Using the distance formula, we have:
Distance = √((6 - (-8))^2 + (-1 - (-2))^2)
Distance = √((6 + 8)^2 + (-1 + 2)^2)
Distance = √(14^2 + 1^2)
Distance = √(196 + 1)
Distance = √197
Distance ≈ 14.04
Therefore, the distance between the points (-8, -2) and (6, -1) is approximately 14.04 units.
To find the midpoint of AB¯¯¯¯¯¯¯¯, we can use the midpoint formula.
The midpoint formula states that the coordinates of the midpoint (x, y) are the average of the coordinates of the endpoints (x₁, y₁) and (x₂, y₂).
So, let's plug in the values:
x = (x₁ + x₂) / 2 = (-3 + -7) / 2 = -10 / 2 = -5
y = (y₁ + y₂) / 2 = (8 + -6) / 2 = 2 / 2 = 1
Therefore, the midpoint of AB¯¯¯¯¯¯¯¯ is (-5, 1).