Question

triangle pqr is located entirely in quadrant ii. which transformation must result in an image of triangle pqr located entirely in quadrant iii?
a reflection over the x - axis
b reflection over the y - axis
c clockwise 90° rotation around the origin
d translation of 5 units down

Explanation:

Step1: Recall coordinate - plane rules

• Reflection over the \(x\) - axis: \((x,y)\to(x, - y)\)
• Reflection over the \(y\) - axis: \((x,y)\to(-x,y)\)
• Clockwise \(90^{\circ}\) rotation about the origin: \((x,y)\to(y, - x)\)
• Translation \(5\) units down: \((x,y)\to(x,y - 5)\)

Step2: Analyze quadrant changes

• Quadrant II has \(x\lt0,y\gt0\). For a triangle to move to Quadrant III (\(x\lt0,y\lt0\)), we need to change the \(y\) - coordinate sign while keeping the \(x\) - coordinate sign.
• Reflection over the \(x\) - axis changes the \(y\) - coordinate sign. If a point \((x,y)\) (\(x\lt0,y\gt0\)) is reflected over the \(x\) - axis, it becomes \((x,-y)\) (\(x\lt0,-y\lt0\)) which is in Quadrant III.

Answer:

A. reflection over the \(x\) - axis