Question

WWhat is the equation for the line of reflection? On a coordinate plane, triangle A B C has points (6, 3.7), (5.4, 2), (1, 3). Triangle A prime B prime C prime has points (3.7, 6), (2, 5.4), (3, 1). x = 3 y = 3 y = x x = 6

Answer 1

c

Explanation:

Answer 2

`y = x`

Explanation:

Given

`A =(6,3.7)`

`B = (5.4,2)`

`C = (1,3)`

`A' = (3.7, 6)`

`B' = (2, 5.4)`

`C' = (3, 1)`

Required

The equation for the line of reflection

Taking points A and A' as a point of reference:

`A =(6,3.7)` and
`A' = (3.7, 6)`

First, calculate the midpoint (M)

`M = ((x_2+x_1)/(2),(y_2+y_1)/(2))`

`M = ((3.7+6)/(2),(6+3.7)/(2))`

`M = ((9.7)/(2),(9.7)/(2))`

`M = (4.85, 4.85)`

Calculate the slope (m)

`m = (y_2 - y_1)/(x_2 - x_1)`

`m = (6 - 3.7)/(3.7 - 6)`

`m = (2.3)/(-2.3)`

`m = -1`

The midpoint of a reflection is always perpendicular to the points being reflected.

So, the slope of
`M = (4.85, 4.85)` is:

`m_2 = -(1)/(m)`

`m_2 = -(1)/(-1)`

`m_2 = 1`

The equation is then calculated as:

`y = m_2(x - x_1) + y_1`

Where:

`(x_1,y_1) = (4.85,4.85)`

`y = 1(x - 4.85) + 4.85`

`y = x - 4.85 + 4.85`

`y = x`

Hence, the equation of line of reflection is:

`y = x`