Question
Triangle ABC has vertical point A (-2,-2), 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 3 and a center point of dilation at the origin.
Answers
GPT 3.5
To find the coordinates of the image points after a dilation with a scale factor of 3 and a center of dilation at the origin, we can use the following formula:
A' = (3 * (xA - origin_x), 3 * (yA - origin_y))
B' = (3 * (xB - origin_x), 3 * (yB - origin_y))
C' = (3 * (xC - origin_x), 3 * (yC - origin_y))
Given points:
A (-2,-2), B (-4,-3), C (-2,-5)
Origin: (0,0)
Calculating the image points:
A' = (3 * (-2 - 0), 3 * (-2 - 0))
A' = (-6, -6)
B' = (3 * (-4 - 0), 3 * (-3 - 0))
B' = (-12, -9)
C' = (3 * (-2 - 0), 3 * (-5 - 0))
C' = (-6, -15)
Therefore, the coordinates of the image points A', B', and C' after a dilation with a scale factor of 3 and a center of dilation at the origin are:
A' (-6, -6)
B' (-12, -9)
C' (-6, -15)
A' = (3 * (xA - origin_x), 3 * (yA - origin_y))
B' = (3 * (xB - origin_x), 3 * (yB - origin_y))
C' = (3 * (xC - origin_x), 3 * (yC - origin_y))
Given points:
A (-2,-2), B (-4,-3), C (-2,-5)
Origin: (0,0)
Calculating the image points:
A' = (3 * (-2 - 0), 3 * (-2 - 0))
A' = (-6, -6)
B' = (3 * (-4 - 0), 3 * (-3 - 0))
B' = (-12, -9)
C' = (3 * (-2 - 0), 3 * (-5 - 0))
C' = (-6, -15)
Therefore, the coordinates of the image points A', B', and C' after a dilation with a scale factor of 3 and a center of dilation at the origin are:
A' (-6, -6)
B' (-12, -9)
C' (-6, -15)