Question

Triangle NMO is drawn with vertices N(−5, 2), M(−2, 1), O(−3 , 3). Determine the image vertices of N′M′O′ if the preimage is reflected over x = −5.

Answer 1

The image vertices after reflecting triangle NMO over the line x = -5 are N′(-5, 2), M′(-8, 1), and O′(-7, 3).

How to reflect an image?

To find the image vertices of N′M′O′ after reflecting over the line x = -5, you can use the formula for reflecting a point over a vertical line.

The reflection of a point (x, y) over the vertical line x = a is given by (2a - x, y).

Let's apply this formula to each vertex:

1. For N(−5, 2):

N' = (2(-5) - (-5), 2) = (-5, 2)

2. For M(−2, 1):

M' = (2(-5) - (-2), 1) = (-8, 1)

3. For O(−3, 3):

O' = (2(-5) - (-3), 3) = (-7, 3)

So, the image vertices after reflecting over x = -5 are N′(-5, 2), M′(-8, 1), and O′(-7, 3).