Question

question: 5
figures j, k, l, m, n, and p are shown on the coordinate plane.
part b
what figure can be transformed into figure l by a 90° rotation clockwise about the origin followed by a translation 2 units down?
a figure j
b figure m
c figure n
d figure p
question: 6
in the coordinate plane shown. figure 1 is congruent to figure 2 and figure 3.
describe a series of transformations to show that figure 1 is congruent to figure 2. include all the necessary information to complete the transformation.

Explanation:

Step1: Understand rotation and translation

A \(90^{\circ}\) clock - wise rotation about the origin \((x,y)\to(y, - x)\). A translation 2 units down \((x,y)\to(x,y - 2)\).

Step2: Analyze each figure

• For figure \(J\): Assume a point \((x,y)\) on \(J\). After \(90^{\circ}\) clock - wise rotation \((x,y)\to(y, - x)\), then after translation 2 units down \((y,-x)\to(y,-x - 2)\). By visual inspection (counting grid units and orientation), when we perform these transformations on \(J\), we can match it with \(L\).
• For figure \(M\): Its shape and orientation after transformation will not match \(L\). The side lengths and angles (by counting grid - based lengths and observing slopes) do not align with the transformation result to get \(L\).
• For figure \(N\): Its shape (a different polygon type compared to \(L\) when considering side - length ratios and angles) does not match the result of the transformation.
• For figure \(P\): Its orientation and side - length relationships (by comparing the lengths of corresponding sides after the transformation rules) do not match \(L\).

Answer:

A. figure J