Question

use the coordinates plotted below.
select all the true statements
a. point g is a translation of point f 6 units up.
b. point f is a reflection of point d across the y - axis.
c. point g is a rotation of point d 180° clockwise around k.
d. point g is a rotation of point d 180° counterclockwise around k.
e. cannot be determined

Explanation:

Step1: Find coordinates

Find the coordinates of each point. Assume \(K=(0,0)\), \(F = (-2,3)\), \(G=(-2,-3)\), \(D=(2,3)\).

Step2: Check option A

For translation, if we translate \(F(-2,3)\) \(6\) units up, the new \(y -\)coordinate is \(3 + 6=9\), not \(-3\). So A is false.

Step3: Check option B

For reflection across \(y -\)axis, the rule is \((x,y)\to(-x,y)\). For \(D(2,3)\), reflection across \(y -\)axis is \((-2,3)\) which is \(F\). So B is true.

Step4: Check option C and D

For a \(180^{\circ}\) rotation (clockwise or counter - clockwise) around the origin \((0,0)\) (point \(K\)), the rule is \((x,y)\to(-x,-y)\). For \(D(2,3)\), \(180^{\circ}\) rotation gives \((-2,-3)\) which is \(G\). So C and D are true.

Answer:

B. Point \(F\) is a reflection of point \(D\) across the \(y -\)axis; C. Point \(G\) is a rotation of point \(D\) \(180^{\circ}\) clockwise around \(K\); D. Point \(G\) is a rotation of point \(D\) \(180^{\circ}\) counterclockwise around \(K\)