Question

8.g.a.2
what are the vertices of triangle abc after triangle abc is reflected across the y-axis?
graph of coordinate plane with triangle abc
options:
○ a(5, 3), b(1, -3), c(-2, 0)
○ a(-5, -3), b(-1, 3), c(2, 0)
○ a(3, -5), b(-3, -1), c(0, 2)
○ a(5, 3), b(-3, 1), c(2, 0)

Explanation:

Step1: Find original vertices

From the graph, original vertices: \( A(-5, 3) \), \( B(-1, -3) \), \( C(2, 0) \)? Wait, no, let's re - check. Wait, reflection over y - axis: rule is \((x,y)\to(-x,y)\). Wait, first, let's find original coordinates. Looking at the graph, point A: x = - 5, y = 3 (since it's 5 units left of y - axis, 3 up). Point B: x=-1, y = - 3? Wait, no, maybe I misread. Wait, the reflection over y - axis formula is \((x,y)\to(-x,y)\). Wait, let's check the options. Let's take original A: suppose A is (-5,3), then after reflection over y - axis, A' should be (5,3). Original B: suppose B is (-1,-3)? No, wait, maybe B is (-1, - 3)? Wait, no, let's look at the options. The first option: A'(5,3), B'(1,-3), C'(-2,0). Wait, let's find original C: C is (2,0), so reflection over y - axis would be (-2,0)? No, wait, reflection over y - axis: (x,y)→(-x,y). So if original C is (2,0), then C' is (-2,0). Original A: if A' is (5,3), then original A is (-5,3). Original B: if B' is (1,-3), then original B is (-1,-3). Let's check the reflection rule: for a point \((x,y)\) reflected over y - axis, the new point \((x',y')\) is given by \(x'=-x\) and \(y' = y\). So if original A is \((-5,3)\), then \(A'=(5,3)\) (since \(x'=-(-5)=5\), \(y' = 3\)). Original B: if original B is \((-1,-3)\), then \(B'=(1,-3)\) (since \(x'=-(-1)=1\), \(y'=-3\)). Original C: if original C is \((2,0)\), then \(C'=(-2,0)\) (since \(x'=-2\), \(y' = 0\)). So the first option matches: \(A'(5,3)\), \(B'(1,-3)\), \(C'(-2,0)\).

Step2: Verify reflection rule

The rule for reflection over the y - axis is \((x,y)\to(-x,y)\). Let's apply this to each original vertex:

• For \(A(-5,3)\): \(x'=-(-5)=5\), \(y' = 3\), so \(A'(5,3)\).
• For \(B(-1,-3)\): \(x'=-(-1)=1\), \(y'=-3\), so \(B'(1,-3)\).
• For \(C(2,0)\): \(x'=-2\), \(y' = 0\), so \(C'(-2,0)\).

This matches the first option.

Answer:

A. \( A'(5, 3) \), \( B'(1, -3) \), \( C'(-2, 0) \)