Question

1. triangle nmp is graphed below. triangle nmp is rotated 180° counterclockwise about the origin to create triangle nmp. what are the coordinates of triangle nmp?

Explanation:

Step1: Recall the rotation rule

When a point \((x,y)\) is rotated \(180^{\circ}\) counter - clockwise about the origin, the new coordinates are \((-x,-y)\).

Step2: Find the coordinates of \(N\)

The coordinates of \(N\) are \((1,5)\). Using the rule \((x,y)\to(-x,-y)\), for \(N(1,5)\), \(N'(- 1,-5)\).

Step3: Find the coordinates of \(M\)

The coordinates of \(M\) are \((9,4)\). Using the rule \((x,y)\to(-x,-y)\), for \(M(9,4)\), \(M'(-9,-4)\).

Step4: Find the coordinates of \(P\)

The coordinates of \(P\) are \((5,1)\). Using the rule \((x,y)\to(-x,-y)\), for \(P(5,1)\), \(P'(-5,-1)\).

Answer:

\(N'(-1,-5),M'(-9,-4),P'(-5,-1)\) (the fourth option)