Question

1. (x,y)→(x, -y)

pre - image image
a(0,0) a( , )
description:
b(1, -2) b( , )
c(-4, -1) c( , )
d(-3, -3) d( , )

Explanation:

Step1: Apply the transformation to point A

Given the transformation $(x,y)\to(x, -y)$ and $A(0,0)$. Substitute $x = 0$ and $y = 0$ into the transformation. We get $A'(0,-0)=A'(0,0)$.

Step2: Apply the transformation to point B

For $B(1,-2)$, substitute $x = 1$ and $y=-2$ into the transformation $(x,y)\to(x, -y)$. Then $B'(1,-(-2))=B'(1,2)$.

Step3: Apply the transformation to point C

For $C(-4,-1)$, substitute $x=-4$ and $y = - 1$ into the transformation. We have $C'(-4,-(-1))=C'(-4,1)$.

Step4: Apply the transformation to point D

For $D(-3,-3)$, substitute $x=-3$ and $y=-3$ into the transformation. So $D'(-3,-(-3))=D'(-3,3)$.
The description of the transformation $(x,y)\to(x, -y)$ is a reflection over the x - axis.

Answer:

Pre - Image	Image
B(1,-2)	B'(1,2)
C(-4,-1)	C'(-4,1)
D(-3,-3)	D'(-3,3)

Description: Reflection over the x - axis.