Line segment AB has endpoints A (−6, 4) and B (−8, 2) . Find the coordinates of A′ and B′ after a dilation with a scale factor of 1/2, centered at the origin.
To find the coordinates of A' and B' after a dilation with a scale factor of 1/2, centered at the origin, we multiply the x and y-coordinates of A and B by the scale factor.
For point A:
x-coordinate of A' = (scale factor)*(x-coordinate of A)
= (1/2)*(-6)
= -3
y-coordinate of A' = (scale factor)*(y-coordinate of A)
= (1/2)*(4)
= 2
So, A' is located at (-3, 2).
For point B:
x-coordinate of B' = (scale factor)*(x-coordinate of B)
= (1/2)*(-8)
= -4
y-coordinate of B' = (scale factor)*(y-coordinate of B)
= (1/2)*(2)
= 1
So, B' is located at (-4, 1).
Therefore, the coordinates of A' are (-3, 2) and the coordinates of B' are (-4, 1).
There is a cordinate plane. Point A is at (2, 3). Point B is at (4, 1). Point A' is at (6, 9). Point B' is at (12, 3). Determine the scale factor used in the dilation of line segment AB, centered at the origin.
To find the scale factor used in the dilation of line segment AB, we can compare the change in distance between the x-coordinates and the y-coordinates of the original points (A and B) to the corresponding change in distance of the dilated points (A' and B').
The change in distance between the x-coordinates of A and B is:
4 - 2 = 2
The change in distance between the x-coordinates of A' and B' is:
12 - 6 = 6
To find the scale factor, we can divide the change in distance of the dilated points by the change in distance of the original points:
Scale factor = Change in distance of dilated points / Change in distance of original points
Scale factor = 6 / 2 = 3
Therefore, the scale factor used in the dilation of line segment AB, centered at the origin, is 3.
There is a coordinate plane. Point A is at (-3, 4). Point B is at (2, -4). Point A' is at (-6, 8). Point B' is at (4, -8). Determine the scale factor used in the dilation of line AB, with a center point of dilation at the origin.
To find the scale factor used in the dilation of line segment AB, centered at the origin, we can compare the change in distance between the x-coordinates and the y-coordinates of the original points (A and B) to the corresponding change in distance of the dilated points (A' and B').
The change in distance between the x-coordinates of A and B is:
2 - (-3) = 5
The change in distance between the x-coordinates of A' and B' is:
4 - (-6) = 10
The change in distance between the y-coordinates of A and B is:
(-4) - 4 = -8
The change in distance between the y-coordinates of A' and B' is:
(-8) - 8 = -16
To find the scale factor, we can divide the change in distance of the dilated points by the change in distance of the original points.
For the x-coordinates:
Scale factor for x = Change in distance of dilated points / Change in distance of original points
= 10 / 5
= 2
For the y-coordinates:
Scale factor for y = Change in distance of dilated points / Change in distance of original points
= -16 / (-8)
= 2
Therefore, the scale factor used in the dilation of line segment AB, with a center point of dilation at the origin, is 2.
Triangle ABC has vertices point A (2,1) , point B (4,3) , and point C (−2,5) . Find the coordinates of A′, B′, and C′ after a dilation with a scale factor of 7 and a center point of dilation at the origin (0,0).
To find the coordinates of A', B', and C' after a dilation with a scale factor of 7 and a center point of dilation at the origin (0,0), we multiply the x and y-coordinates of each vertex by the scale factor.
For point A:
x-coordinate of A' = (scale factor)*(x-coordinate of A)
= 7*(2)
= 14
y-coordinate of A' = (scale factor)*(y-coordinate of A)
= 7*(1)
= 7
So, A' is located at (14, 7).
For point B:
x-coordinate of B' = (scale factor)*(x-coordinate of B)
= 7*(4)
= 28
y-coordinate of B' = (scale factor)*(y-coordinate of B)
= 7*(3)
= 21
So, B' is located at (28, 21).
For point C:
x-coordinate of C' = (scale factor)*(x-coordinate of C)
= 7*(-2)
= -14
y-coordinate of C' = (scale factor)*(y-coordinate of C)
= 7*(5)
= 35
So, C' is located at (-14, 35).
Therefore, the coordinates of A' are (14, 7), the coordinates of B' are (28, 21), and the coordinates of C' are (-14, 35).
Triangle ABC has vertices point A (2, 1) , point B (−2, 2) , and point C (−3,−1) . After dilation, triangle A′B′C′ has vertices point A′ (4, 2) , point B′ (−4, 4) , and point C′ (−6,−2) . Determine the scale factor for the dilation of triangle ABC with a center point of dilation at the origin (0, 0 ).
To find the scale factor for the dilation of triangle ABC, we can compare the change in distance between the x-coordinates and the y-coordinates of the original triangle (A, B, C) to the corresponding change in distance of the dilated triangle (A', B', C').
The change in distance between the x-coordinates of A and B is:
(-2) - 2 = -4
The change in distance between the x-coordinates of A' and B' is:
(-4) - 4 = -8
The change in distance between the y-coordinates of A and B is:
2 - 1 = 1
The change in distance between the y-coordinates of A' and B' is:
4 - 2 = 2
To find the scale factor, we can divide the change in distance of the dilated triangle by the change in distance of the original triangle.
For the x-coordinates:
Scale factor for x = Change in distance of dilated triangle / Change in distance of original triangle
= (-8) / (-4)
= 2
For the y-coordinates:
Scale factor for y = Change in distance of dilated triangle / Change in distance of original triangle
= 2 / 1
= 2
Since the scale factor is the same for both the x and y-coordinates, the scale factor for the dilation of triangle ABC with a center point of dilation at the origin is 2.
Question 5 of the Dilations Quick Check on Connexus.
Describe the dilation of triangle ABC, with a scale factor of 5 and a center point of dilation at the origin (0, 0).
The answers to the questions are below this text.
1.) Triangle A′B′C′ is 5 times as large as triangle ABC and is 5 times closer to the center point of dilation.
2.) Triangle A'B'C' is 5 times as large as triangle ABC is 5 times as far from the center point of dilation.
3.) Triangle A′B′C′ is 5 times smaller than triangle ABC and is 5 times closer to the center point of dilation.
4.) Triangle A'B'C' is 5 times smaller than triangle ABC is 5 times as far from the center point of dilation.