Question

A triangle with the coordinates X(3, 2), Y(5, -1), and Z(-2, 3) is reflected across both the x- and y-axes. The coordinates after both reflections are what

Answer 1

The coordinates of the reflected triangle are
`X'(x,y) = (-3,-2)`,
`Y' (x,y) = (-5,1)` and
`Z'(x,y) = (2,-3)`.

Explanation:

Let be a point
`(a,b)\in\mathbb{R}^(2)`, reflections across x- and y-axes are represented by the following operations:

x-Axis reflection:

`d = d'`

`b - 0 = 0 - b'`

`b' = -b`

y-Axis reflection:

`d = d'`

`a - 0 = 0 - a'`

`a' = -a`

If we know that
`X (x,y) = (3,2)`,
`Y(x,y) = (5,-1)` and
`Z (x,y) = (-2, 3)`, the coordinates after both reflections are, respectively:

`X'(x,y) = (-3,-2)`

`Y' (x,y) = (-5,1)`

`Z'(x,y) = (2,-3)`

The coordinates of the reflected triangle are
`X'(x,y) = (-3,-2)`,
`Y' (x,y) = (-5,1)` and
`Z'(x,y) = (2,-3)`.