Question

1. triangle mno has vertices m(3,0), n(5,2) and o(1,4). the triangle is translated by (x - 3,y - 1), reflected across the x - axis, and then rotated 180 degrees about the origin. what are the coordinates of vertex n?

• a) (-2,-1)
• b) (2,-1)
• c) (-2,1)
• d) (2,1)

a) (-2,-1)
b) (2,-1)
c) (-2,1)
d) (2,1)

Explanation:

Step1: Apply the translation

The translation rule is $(x,y)\to(x - 3,y - 1)$. For point $N(5,2)$, we have $x = 5$ and $y=2$. After translation, $x'=5 - 3=2$ and $y'=2 - 1 = 1$. So the new - point after translation is $N_1(2,1)$.

Step2: Apply the reflection across the x - axis

The rule for reflecting a point $(x,y)$ across the x - axis is $(x,y)\to(x,-y)$. For point $N_1(2,1)$, after reflection across the x - axis, the new point is $N_2(2,-1)$.

Step3: Apply the 180 - degree rotation about the origin

The rule for rotating a point $(x,y)$ 180 degrees about the origin is $(x,y)\to(-x,-y)$. For point $N_2(2,-1)$, after rotation, $x''=-2$ and $y'' = 1$. So the final point $N'$ is $(-2,1)$.

Answer:

C. (-2,1)