Question

Flecting points in the coordinate plane

What point do we get when we reflect A across the y-axis?
y
9-
B
8
MR
7
6
As
5
4-
E
MY
3
2
A
Co
+
&
7-6
+
9
2
34
5
6 7
2
o
MY
-3-
D
-4-
5
Pro
Pro

Answer 1

E(-9, 2)

Explanation:

The line of reflection is is the perpendicular bisector of the segment between the original point and its reflected image.

In the figure, the y-axis is halfway between points A and E, and is a vertical line perpendicular to the horizontal segment AE. Point E has the same y-coordinate as point A, but its x-coordinate has the opposite sign.

(x, y) ⇒ (-x, y) . . . . . . reflection across the y-axis

A(9, 2) ⇒ E(-9, 2) . . . . reflection of point A across the y-axis

You get point E when you reflect A across the y-axis.

__

Additional comment

When A is reflected across the line y=x, it becomes point B. When it is reflected across the origin, it becomes point C. Reflection across the x-axis maps point A to point D.

(x, y) ⇒ (y, x) . . . . reflection across y=x

(x, y) ⇒ (-x, -y) . . . reflection across the origin

(x, y) ⇒ (x, -y) . . . . reflection across the x-axis

(x, y) ⇒ (-y, -x) . . . reflection across the line y = -x