Question

41. What is the image of O(- 3, - 2) after two reflections, first across the line y = - 5 , then across the line x = 1 ? (1 point) A(-3,-8)

B(-3,-2)
C (5,-2)
D(5,8)
D is correct please show me steps on why

Answer 1

D(5,-8)

Explanation:

The given point is (-3,-2)

When we reflect in the line y=k, we use the rule (x, 2k-y)

This implies that:

`(-3, - 2)\to (-3, 2*-5--2)`

`(-3, - 2)\to (-3, - 8)`

When we reflect in the line x=k, we use the rule

`(x,y)\to (2k-x,y)`

Now we have x=1

This implies that:

`( - 3, - 8)\to (2 * 1- - 3, - 8)`

`( - 3, - 8)\to (5, - 8)`