Question

Segment AB has points A at (2, -5) and B at (5, -3).

Segment AB is reflected across the y-axis and then translated 3 units right.

What are the coordinates of the endpoints on the image A'B'?

Answer 1

Given:

Segment AB has points A at (2,-5) and B at (5,-3)

Segment AB is reflected across the y - axis and then translated 3 units right.

We need to determine the coordinates of the endpoints on the image A'B'

Reflection across the y - axis:

The rule to reflect the coordinates across the y - axis is given by

$(x,y)\rightarrow (-x,y)$

Thus, the reflection of the point A is given by

$A(2,-5)\rightarrow A(-2,-5)$

The reflection of the point B is given by

$B(5,-3)\rightarrow B(-5,-3)$

Therefore, the reflection of the points A and B across the y - axis are (-2,-5) and (-5,-3) respectively.

Shifting 3 units to the right:

The rule to shift the coordinates to the right is given by

$(x,y)\rightarrow (x+h,y)$

The point A is shifted 3 units to the right is given by

$A(-2,-5)\rightarrow (-2+3,-5)\rightarrow A'(1,-5)$

The point B is shifted 3 units to the right is given by

$B(-5,-3)\rightarrow (-5+3,-3)\rightarrow B'(-2,-3)$

Hence, the coordinates of the endpoints on the image A' and B' are (1,-5) and (-2,-3)