Question

for a point at (2, -3), which new coordinates could it have after a sequence involving a 180-degree rotation and a reflection across the x-axis?
a. (2, -3)
b. (-2, -3)
c. (2, 3)
d. (-2, 3)

a rectangle is rotated 90 degrees clockwise around the origin. if one vertex starts at (1, 2), what will be its new coordinates after rotation?
a. (2, -1)
b. (1, -2)
c. (-1, 2)
d. (2, 1)

Explanation:

First Question:

Step1: 180° rotation rule

For a point \((x,y)\), 180° rotation gives \((-x,-y)\). So \((2,-3)\) becomes \((-2,3)\).

Step2: Reflect across x - axis

Reflection across x - axis: \((x,y)\to(x,-y)\). So \((-2,3)\) becomes \((-2,-3)\).

Step1: 90° clockwise rotation rule

For a point \((x,y)\), 90° clockwise rotation around origin gives \((y,-x)\).

Step2: Apply to (1,2)

Substitute \(x = 1,y = 2\) into \((y,-x)\), we get \((2,-1)\).

Answer:

b. (-2, -3)

Second Question: