Question

Which translation will change figure ABCD to figure A'B'C'D'?

Answer 1

@ms.hi

Looking at the pre-image points A, B, C, and D, I viewed the coordinates of those points in contrast with the coordinates of the corresponding image points A', B', C', and D'.

A (4,-2) A' (-4,5)
B (6,-4) B' (-2, 3)
C (2, -5) C' (-6,2)
D (2, -3) D" (-6, 4)

We are looking for a formula of sorts to indicate the mapping or translation of the points of Quad ABCD to Quad A'B'C'D'

Answer 2

Looking at points A and A'
A (4,-2) A' (-4,5)

I wrote 4 + k = -4 and solved for k to be -8

The same vale of k, -8, added to each x-coordinate of the remaining 3 points gave the x coordinate of the image point.

So far, we know that the translation looks like this (x,y) --> (x - 8, ?)

Answer 3

Looking at the y-coordinates of points A and A'

A (4,-2) A' (-4,5)

I wrote -2 + c = 5 and solved for c to be +7

The same vale of c, +7, added to each y-coordinate of the remaining 3 points gave the y coordinate of the image point.

Therefore, we know that the translation looks like this: (x,y) --> (x - 8, y + 7)

The two quadrilaterals are congruent because this mapping preserves size and shape.

Do ask if you have questions, okay?