Question

solve the problems below. show all work.
g. triangle hjk is shown on the coordinate grid. a student reflected triangle hjk over the x - axis to create triangle hjk. what rule describes this transformation?
j. parallelogram abcd is translated 7 units to the right to create parallelogram abcd. what rule describes this transformation?
l. trapezoid klmn is rotated 270° clockwise about the origin to create parallelogram klmn. what rule describes this transformation?

Explanation:

Step1: Recall reflection rule over x - axis

For a point $(x,y)$ reflected over the x - axis, the x - coordinate remains the same and the y - coordinate changes its sign. So the rule is $(x,y)\to(x, - y)$.

Step2: Recall translation rule for right - shift

For a translation of a point $(x,y)$ 7 units to the right, we add 7 to the x - coordinate and the y - coordinate remains the same. The rule is $(x,y)\to(x + 7,y)$.

Step3: Recall 270 - degree clockwise rotation rule

A 270 - degree clockwise rotation about the origin is equivalent to a 90 - degree counter - clockwise rotation. For a point $(x,y)$ rotated 90 degrees counter - clockwise about the origin, the rule is $(x,y)\to(-y,x)$.

Answer:

G. $(x,y)\to(x, - y)$
J. $(x,y)\to(x + 7,y)$
L. $(x,y)\to(-y,x)$