Question

The image of the origin under a reflection in the line y = x + 2 is point A. On a sheet of graph paper, (i) draw the line y = x + 2, (ii) find the coordinates of A.​

Answer 1

Step-by-step explanation:

We must rotate point (0,0) across line y=x+2.

First, we need a line that is perpendicular through y=x+2 and passess through 0,0

The slope is -1 so we have

$y - 0 = - 1(x - 0)$

$y = - x$

So the slope perpendicular to that line is y=-x.

Next, the we must find where they intersect at.

$- x = x + 2$

$- 2 = 2x$

$x = - 1$

$- ( - 1) = 1$

So they intersect at -1,1.

Next, the point of intersection is the midpoint and the orgin is endpoint and the image of A is the other endpoint.

The x coordinate of the image of A is -2, and the y coordinate is 2.

So the answer is (-2,2)

Your graph is above.