Question

30284_geo module 4_graph
refer to the graph.

1. what are the coordinates of the triangle after it is reflected in y = -x?

a. d(5,8), e(9,6), f(3,1)
b. d(-5,-8), e(-9,-6), f(-3,-1)
c. d(8,-5), e(6,-9), f(1,-3)
d. d(-8,5), e(-6,9), f(-1,3)

Explanation:

Step1: Identify Original Coordinates

From the graph, original points: \( D(-5, -8) \)? Wait, no, looking at the labels: \( D(-8, -5) \), \( E(-6, -9) \), \( F(-1, -3) \)? Wait, no, the labels: \( D(-8, -5) \)? Wait, the graph has \( D(-8, -5) \), \( E(-6, -9) \), \( F(-1, -3) \)? Wait, the reflection over \( y = -x \)? Wait, no, the question is reflection over \( y = x \)? Wait, the problem says "reflected in \( y = -x \)"? Wait, no, the user's question: "reflected in \( y = x \)"? Wait, no, let's check the options. Wait, the original points: from the graph, \( D(-8, -5) \)? Wait, no, the labels: \( D(-8, -5) \), \( E(-6, -9) \), \( F(-1, -3) \)? Wait, reflection over \( y = -x \) has the rule \( (x, y) \to (-y, -x) \). Wait, no, reflection over \( y = x \) is \( (x, y) \to (y, x) \). Wait, let's check the original coordinates. From the graph, \( D(-8, -5) \)? Wait, no, the labels: \( D(-8, -5) \)? Wait, the first label: \( D(-8, -5) \), \( E(-6, -9) \), \( F(-1, -3) \)? Wait, let's check the reflection over \( y = -x \): the rule is \( (x, y) \to (-y, -x) \). So for \( D(-8, -5) \): \( (-(-5), -(-8)) = (5, 8) \)? No, that's not. Wait, maybe reflection over \( y = x \): \( (x, y) \to (y, x) \). So \( D(-8, -5) \to (-5, -8) \)? No, option B is \( D'(-5, -8) \), \( E'(-9, -6) \), \( F'(-3, -1) \). Wait, original \( D(-8, -5) \), \( E(-6, -9) \), \( F(-1, -3) \). Reflection over \( y = x \) swaps x and y: \( D(-8, -5) \to (-5, -8) \), \( E(-6, -9) \to (-9, -6) \), \( F(-1, -3) \to (-3, -1) \). Which matches option B.

Step2: Verify Each Point

• For \( D(-8, -5) \), reflection over \( y = x \) gives \( (-5, -8) \).
• For \( E(-6, -9) \), reflection gives \( (-9, -6) \).
• For \( F(-1, -3) \), reflection gives \( (-3, -1) \).

This matches option B.

Answer:

B. D'(-5, -8), E'(-9, -6), F'(-3, -1)