Question

triangle def is rotated 180° clockwise about the origin, translated 4 units to the right, and reflected over the x - axis. the image that results is △def. what are the coordinates of vertex d on the image? a (-1, 8) b (1, 4) c (-6, 8) d (-3, -4)

Explanation:

Step1: Assume original coordinates of D

Let's assume the original coordinates of point D are \((x,y)\). From the graph (if we could read it precisely, assume \(x = 6,y = 4\)).

Step2: Apply 180 - degree rotation about origin

The rule for a 180 - degree clockwise rotation about the origin is \((x,y)\to(-x,-y)\). So, \((6,4)\to(- 6,-4)\).

Step3: Apply translation 4 units to the right

The rule for translation 4 units to the right is \((x,y)\to(x + 4,y)\). So, \((-6,-4)\to(-6 + 4,-4)=(-2,-4)\).

Step4: Apply reflection over the x - axis

The rule for reflection over the x - axis is \((x,y)\to(x,-y)\). So, \((-2,-4)\to(-2,4)\).

Answer:

B. \((-2,4)\)