Question

Write the coordinates of the vertices after a reflection over the line x=-2

d(-10,0)
e(-10,2)
f(-5,2
g(-5,0)

Answer 1

Given:

The vertices are d(-10,0), e(-10,2), f(-5,2) and g(-5,0).

To find:

The coordinates of the vertices after reflection over the line x=-2.

Solution:

If figure reflected over the line x=a, then

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

Here, the figure is reflected over the line x=-2, then

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

`(x,y)\to (-4-x,y)` ...(i)

Now,

For point d,

`(-10,0)\to (-4-(-10),0)`

`(-10,0)\to (-4+10,0)`

`(-10,0)\to (6,0)`

Similarly,

For point e,

`(-10,2)\to (-4-(-10),2)=(6,2)`

For point f,

`(-5,2)\to (-4-(-5),2)=(1,2)`

For point g,

`(-5,0)\to (-4-(-5),0)=(1,0)`

Therefore, the coordinates of vertices after a reflection over the line x=-2 are d prime (6,0), e prime (6,2), f prime, (1,2) and g prime (1,0).