Question

24 (a)
figures j, k, l, m, n, and p are shown on the coordinate plane.
part a
which figure can be transformed into figure p by a translation 2 units to the right followed by a reflection across the x - axis?
a figure j
b figure k
c figure l
d figure m
(b)
part b
which 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

Explanation:

Part A

To determine which figure transforms into \( P \) via translation 2 units right and reflection over \( x \)-axis, analyze each option:

• Figure \( J \): Translation 2 right + \( x \)-axis reflection doesn’t match \( P \)’s shape/orientation.
• Figure \( K \): Translation 2 right + \( x \)-axis reflection doesn’t align with \( P \).
• Figure \( L \): Translation 2 right + \( x \)-axis reflection doesn’t match \( P \).
• Figure \( M \): Translate \( M \) 2 units right (shifts horizontally), then reflect over \( x \)-axis (flips vertically). This matches \( P \)’s position/shape.

To find the figure transforming into \( L \) via \( 90^\circ \) clockwise rotation (about origin) + translation 2 units down:

• Figure \( J \): \( 90^\circ \) clockwise rotation + 2 down doesn’t match \( L \).
• Figure \( M \): \( 90^\circ \) clockwise rotation + 2 down doesn’t align with \( L \).
• Figure \( N \): \( 90^\circ \) clockwise rotation (changes orientation) + 2 units down. This matches \( L \)’s position/shape.
• Figure \( P \): \( 90^\circ \) clockwise rotation + 2 down doesn’t match \( L \).

Answer:

D. figure \( M \)

Part B