Question

△abc is rotated 90° clockwise around the origin to form △abc. which coordinate is the same as the x-coordinate of point a? y-coordinate of point a which coordinate is the same as the y-coordinate of point a? x-coordinate of point a y-coordinate of point a opposite of x-coordinate of point a opposite of y-coordinate of point a a (-1,2) a (2,1)

Explanation:

Step1: Recall 90° clockwise rotation rule

For a point \((x, y)\), rotating 90° clockwise around the origin gives \((y, -x)\)? Wait, no, wait: Wait, correct rule: 90° clockwise rotation: \((x, y) \to (y, -x)\)? Wait, no, let's check point A: A is \((-1, 2)\), A' is \((2, 1)\). Let's see: Original A: \(x = -1\), \(y = 2\). A' has \(x = 2\), \(y = 1\). Wait, 90° clockwise rotation formula is \((x, y) \to (y, -x)\)? Wait, no, \((-1, 2)\) rotated 90° clockwise: \(x\) becomes \(y\) (2), \(y\) becomes \(-x\) (1, since -(-1)=1). Yes, so \((-1, 2) \to (2, 1)\), which matches A'.

Step2: Analyze y-coordinate of A'

Point A: \((-1, 2)\), so \(x_A = -1\), \(y_A = 2\). A' is \((2, 1)\), so \(y_{A'} = 1\). The opposite of \(x_A\) is \(-(-1) = 1\), which matches \(y_{A'}\). Let's check options:

• \(x\)-coordinate of A: \(-1\) ≠ 1.
• \(y\)-coordinate of A: 2 ≠ 1.
• Opposite of \(x\)-coordinate of A: \(-(-1) = 1\), which matches \(y_{A'}\).
• Opposite of \(y\)-coordinate of A: \(-2\) ≠ 1.

Answer:

Opposite of \(x\)-coordinate of point \(A\)