Question

2015 > chapter 4 > section exercises 4.3 > exercise 8
graph △def and its image after a rotation 180° about the origin
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8

Explanation:

Step1: Find coordinates of \( \triangle DEF \)

Assume \( D(-4,-1) \), \( E(-3,2) \), \( F(3,-2) \) (by observing the graph).

Step2: Apply rotation rule

The rule for a \( 180^{\circ} \) rotation about the origin is \( (x,y)\to(-x,-y) \).

• For \( D(-4,-1) \): \( (-(-4),-(-1))=(4,1) \)
• For \( E(-3,2) \): \( (-(-3),-2)=(3,-2) \)
• For \( F(3,-2) \): \( (-3,2) \)

Answer:

Plot \( \triangle DEF \) with vertices \( D(-4,-1) \), \( E(-3,2) \), \( F(3,-2) \) and its image \( \triangle D'E'F' \) with vertices \( D'(4,1) \), \( E'(3,-2) \), \( F'(-3,2) \) on the coordinate plane.