Question

Triangle ABC has vertices located at A(1, -4), B(4, -6) and C(2, -1) on a coordinate grid. After it is reflected across the y-axis and a dilation of ½ is applied, what is the new coordinate of B? A. (4,6) B. (8,12) C. (2,3) D (-2, -3)

Answer 1

`B' = (-2,-3)`

Explanation:

Given

`A = (1,-4)`

`B = (4,-6)`

`C = (2,-1)`

reflection across y

`d = (1)/(2)`

Required

New coordinate of B

When reflected across the y-axis.

The rule is:

`(x,y) \to (-x,y)`

So:

`(4,-6) \to (-4,-6)`

Next is a dilation by 1/2

To do this, we multiply the new point by 1/2

So:

`B' = (-4,-6) * (1)/(2)`

`B' = (-4* (1)/(2),-6* (1)/(2))`

`B' = (-2,-3)`