How do you know what quadrant these two are in? I'm having a little trouble determining. Can someone check if my answers are correct for all and help me fix it to make it right.
10.) The point is on the x-axis and 12 units to the left of the y-axis.
My answer: (0, -12)
12.) y<-5 = Quadrant 3
16.) xy<0 = Quadrant 1
26.) (-3, -1) & (2,-1)
Find distance.
My answer: 5
30.) the 3 points of the triangle they gave are (1,5), (5,-2), & (1,-2)
Find the length of each side of the right triangle & show that these lengths satisfy the pythagorean theorem.
??
42.) (-1,2) & (5,4)
Distance answer= square root 40
midpoint= 2,3)
47.) (-16.8, 12.3) & (5.6, 4.9)
Distance answer= square root 556.52 or 23.6
Midpoint= (-5.6, 8.6)
Are These Right??
I'm kinda suck on #30!!
10. Any point on the x-axis has a Y of 0;
12 units to the left of the Y-axis is an
X value (-)12: P(-12,0).
12. Q3, or Q4 depending on whether X is
positive or negative.
16. X,Y < 0. Q3.
26. (-3,-1), (2,-1).
D^2 = X^2 + Y^2 = (2+3)^2 + (-1+1)^2 =
25 + 0 = 25.
D = 5.
30. (1,5), (5,-2), (1,-2).
First, sketch the triangle showing the
given points.
The vertical side: (1,5), (1,-2).
L^2 = X^2 + Y^2 = (1-1)^2 + (-2-5)^2 =
0 + 49 = 49.
L = 7. or 5-(-2) = 5 + 2 = 7.
Horizontal side: (1,-2), (5,-2).
L = 5-1 = 4.
Hyp : (1,5), (5,-2).
L^2 = (5-1)^2 + (-2-5)^2 =
Use the length of the hor. and ver. sides to calculate length of hyp.
L^2 = X^2 + Y^2 .
42. (-1,2),(x,y), (5,4).
D^2 = (5+1)^2 + (4-2)^2
Mid-point:
(5+1) = 2(x+1).
Solve for X.
(4-2) = 2(y-2).
Solve for Y.
47. Same procedure as #42.
To determine the quadrant in which a point is located, you need to consider the signs of the x and y coordinates. Here is how you can determine the quadrant for each of the points mentioned:
10.) The point is on the x-axis and 12 units to the left of the y-axis.
Since the point lies on the x-axis, the y-coordinate is 0. The fact that it is 12 units to the left of the y-axis indicates that the x-coordinate is negative. Hence, the point is in the fourth quadrant. The correct answer is (x, y) = (-12, 0).
12.) y<-5 = Quadrant 3
The inequality states that the y-coordinate is less than -5. Since there is no information given about the x-coordinate, it can be positive or negative. Hence, the point can be in either the third or fourth quadrant.
16.) xy<0 = Quadrant 1
The inequality xy < 0 means that the product of x and y is negative. To satisfy this condition, one of the coordinates must be negative while the other is positive. Hence, the point lies in the second quadrant.
26.) (-3, -1) & (2, -1)
To find the distance between these two points, you can use the distance formula:
Distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Plugging in the values, we get:
Distance = sqrt((2 - (-3))^2 + (-1 - (-1))^2)
Simplifying further:
Distance = sqrt(5^2 + 0^2)
Distance = sqrt(25)
Distance = 5
So your answer of 5 is correct.
30.) The 3 points of the triangle they gave are (1, 5), (5, -2), and (1, -2)
To find the length of each side of the right triangle, you can use the distance formula between each pair of points. Let's name the points A(1, 5), B(5, -2), and C(1, -2). The sides of the triangle are AB, BC, and AC.
The length of AB = sqrt((x2 - x1)^2 + (y2 - y1)^2) = sqrt((5 - 1)^2 + (-2 - 5)^2) = sqrt(16 + 49) = sqrt(65).
The length of BC = sqrt((x2 - x1)^2 + (y2 - y1)^2) = sqrt((5 - 1)^2 + (-2 - (-2))^2) = sqrt(16 + 0) = sqrt(16) = 4.
The length of AC = sqrt((x2 - x1)^2 + (y2 - y1)^2) = sqrt((1 - 1)^2 + (-2 - 5)^2) = sqrt(0 + 49) = sqrt(49) = 7.
To verify if these lengths satisfy the Pythagorean theorem, we need to check if the sum of the squares of the two shorter sides is equal to the square of the longest side. In this case, AB^2 + BC^2 should equal AC^2. Let's confirm:
(sqrt(65))^2 + 4^2 = 65 + 16 = 81 = (sqrt(7))^2
Therefore, the lengths satisfy the Pythagorean theorem.
42.) (-1, 2) & (5, 4)
To find the distance between these two points, you can use the distance formula as mentioned earlier. Plugging in the values, we get:
Distance = sqrt((5 - (-1))^2 + (4 - 2)^2) = sqrt(6^2 + 2^2) = sqrt(36 + 4) = sqrt(40)
So your answer of square root 40 is correct.
To find the midpoint, you can use the midpoint formula:
Midpoint = ((x1 + x2)/2, (y1 + y2)/2) = ((-1 + 5)/2, (2 + 4)/2) = (2/2, 6/2) = (1, 3).
So your answer of (2, 3) is not correct; the correct midpoint is (1, 3).
47.) (-16.8, 12.3) & (5.6, 4.9)
To find the distance between these two points, you can use the distance formula as mentioned earlier. Plugging in the values, we get:
Distance = sqrt((5.6 - (-16.8))^2 + (4.9 - 12.3)^2) = sqrt(22.4^2 + (-7.4)^2) = sqrt(501.76 + 54.76) = sqrt(556.52) ≈ 23.6 (rounded to one decimal place)
So your distance answer of square root 556.52 or 23.6 is correct.
To find the midpoint, you can use the midpoint formula:
Midpoint = ((x1 + x2)/2, (y1 + y2)/2) = ((-16.8 + 5.6)/2, (12.3 + 4.9)/2) = (-11.2/2, 17.2/2) = (-5.6, 8.6)
So your midpoint answer of (-5.6, 8.6) is correct.
I hope this helps! Let me know if you have any more questions.