Question

Triangle ABC is reflected over the line y=x triangle ABC has points (-6,-1)(-2,-1) and (-5,-6) what is the C coordinate

Answer 1

`\boxed{(-6,-5)}}`

Explanation:

When you reflect a point (x, y) across the line y = x, the coordinates get interchanged. Thus,

(a,b) ⟶ (b,a)

Here are the coordinates of your triangle before and after the reflection.

`\begin{array}{rcl}\textbf{Before} & & \textbf{After}\\A(-6,-1) & \longrightarrow \, & A'(-1,-6)\\B(-2,-1) & \longrightarrow \, & B'(-1,-2)\\C(-5,-6) & \longrightarrow \, & C'(-6,-5)\\\end{array}`

The diagram below shows ∆ABC with its reflection ∆A'B'C'.

`\text{The coordinates of C' have become } \boxed{\mathbf{(-6,-5)}}`

Answer 2

C' = (-6, -5)

Explanation:

We are given that a triangle ABC is reflected over the line y = x.

Given the points of the vertices of the triangle ABC to be (-6, -1) (-2, -1) and (-5, -6) respectively, we are to determine the coordinates of C'.

When reflected over the line y = x, the x and y coordinates exchange their place.

(x, y) ---> (y, x)

Therefore, if C = (-5,-6) then C' = (-6, -5).