For the point ( -3, 1), determine the points that are symmetric with respect to (a) the x axis..?

Question

...that are symmetric with (a) the x axis, (b) the y axis, and (c) the origin.

I have no clue how to do this...I need some help 4realz...

Answer 1

a) (-3, -1). "Symmetric with the x-axis" is sort of like saying that the x-axis is a mirror and you want to show where the reflection of the point would be. When you reflect a point across the x-axis, its y-value is negated (1 -> -1).

b) (3, 1). Similar for the y-axis -- when you reflect a point across the y-axis, its x-value is negated (-3 -> 3).

c) (3, -1). When you reflect a point through the origin, you want something that is on the exactly opposite side of the origin from the given point, and also the exact same distance away. This is done by negating BOTH its x-value and y-value (-3 -> 3, 1 -> -1) -- so it's the same as reflecting across BOTH the y-axis and then the x-axis.

Answer 2

Okay I get it. At first I was like, what?! Now I get it. They are asking you to find the point that makes it symmetrical with respect to each part of the question. First, graph -3,1 on the graph. A simple graph will do to help you visualize.
a) We need to find the point that will make it symmetrical to the x axis, hence what point can we make where we can cut the graph in half across the x axis to make mirror images. That will be -3,-1.
b) 3,1
c) 3,-1

Answer 3

(-3,1) is 1 unit above the x-axis, and 3 units to the left of the y-axis

so something symmetric to the x-axis is (-3,-1)

Answer 4

To find any point symmetric to (x,y) along x-axis, change y to -y and to find any point symmetric along y-axis, change x to -x and to find point symmetric along origin, change both x and y to -x and -y.

So point symmetric point of (-3,1) along x-axis is (-3,-1), along y-axis is (3,1) and along origin is (3,-1)

Answer 5

reflect it over each axis
x (3,1)
y (-3,-1)
O (-3,1)