Question

geometry - hellis
topic 3: readiness assessment
due
oct 23 - 3:00 pm
late
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: Analyze Option A

Point \(F(-2,3)\), point \(G(-2,-3)\). The vertical distance between them is \(3 - (-3)=6\) units down, not up. So A is false.

Step2: Analyze Option B

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

Step3: Analyze Option C

Rotation of \(180^{\circ}\) clockwise around \(K(0,0)\) has the rule \((x,y)\to(-x,-y)\). Point \(D(2,3)\) after \(180^{\circ}\) clockwise rotation around \(K\) is \((-2,-3)\) which is point \(G\). So C is true.

Step4: Analyze Option D

Rotation of \(180^{\circ}\) counter - clockwise around \(K(0,0)\) also has the rule \((x,y)\to(-x,-y)\). Point \(D(2,3)\) after \(180^{\circ}\) counter - clockwise rotation around \(K\) is \((-2,-3)\) which is point \(G\). So D is 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 \(K\)