Question

△abc is reflected across the x - axis and then translated 4 units up to create △abc. what are the coordinates of the vertices of △abc?
a. a(-3,3), b(-1,1), c(-2,3)
b. a(3,-3), b(1,-1), c(2,-3)
c. a(3,-5), b(1,-7), c(3,-5)
d. a(-3,3), b(-1,1), c(-2,-3)

Explanation:

Step1: Find original coordinates

From the graph, \( A(-3, 1) \), \( B(-1, 3) \), \( C(-2, 1) \).

Step2: Reflect over x - axis

Rule for reflection over x - axis: \((x,y)\to(x, -y)\).

• For \( A(-3,1) \): \( A_1(-3,-1) \)
• For \( B(-1,3) \): \( B_1(-1,-3) \)
• For \( C(-2,1) \): \( C_1(-2,-1) \)

Step3: Translate 4 units up

Rule for translation 4 units up: \((x,y)\to(x,y + 4)\).

• For \( A_1(-3,-1) \): \( A'(-3,-1 + 4)=(-3,3) \)
• For \( B_1(-1,-3) \): \( B'(-1,-3 + 4)=(-1,1) \)
• For \( C_1(-2,-1) \): \( C'(-2,-1 + 4)=(-2,3) \) (Wait, but let's check the options. Wait, maybe I misread the original coordinates. Wait, looking at the options, option A is \( A'(-3,3), B'(-1,1), C'(-2,3) \)? Wait, no, wait the options:

Wait the options are:

A. \( A'(-3,3), B'(-1,1), C'(-2,3) \)

Wait let's re - check the reflection and translation:

Original coordinates: From the graph, \( A(-3,1) \), \( B(-1,3) \), \( C(-2,1) \)

Reflection over x - axis: \((x,y)\to(x,-y)\)

\( A(-3,1)\to(-3,-1) \)

\( B(-1,3)\to(-1,-3) \)

\( C(-2,1)\to(-2,-1) \)

Then translate 4 units up: add 4 to y - coordinate.

\( A(-3,-1 + 4)=(-3,3) \)

\( B(-1,-3 + 4)=(-1,1) \)

\( C(-2,-1 + 4)=(-2,3) \)

Which matches option A.

Answer:

A. \( A'(-3, 3), B'(-1, 1), C'(-2, 3) \)