Question

select the graph of the image of (\triangle def) after a (270^{circ}) rotation about (d) followed by a translation along (langle 2,-1
angle)

Explanation:

Step1: Analyze the rotation

A \(270^{\circ}\) rotation about a point changes the orientation of the triangle. The general rule for a \(270^{\circ}\) rotation about the origin \((x,y)\to(y, -x)\), but since it's about point \(D\), we consider the relative positions. After rotation, the triangle will have a new orientation relative to \(D\).

Step2: Analyze the translation

The translation vector \(\langle2,-1
angle\) means we move each point of the rotated triangle \(2\) units to the right (in the \(x\)-direction) and \(1\) unit down (in the \(y\)-direction).

Step3: Check each option

• Option A: Incorrect orientation and translation.
• Option B: Incorrect translation direction (down - wrong relative to rotation effect).
• Option C: Correctly shows the \(270^{\circ}\) rotation about \(D\) followed by \(\langle2,-1

angle\) translation.

• Option D: Incorrect as it seems to have a wrong combination (maybe a reflection or wrong - step transformation).

Answer:

C.