Question

if k > 0, then mn > mn.
if k > 1, then mn > mn.
if 0 < k < 1, then mn < mn.
if 0.5 < k < 1.5, then mn < mn.
if k = 1, then mn = mn.
if k = 0.5, then mn = 0.5(mn).
part b (3 points):
on the coordinate plane to the right, showcase one correct statement (from part a --> statements a - d only).
label m, n, m, and n on the graph.
identify the value of k, as well as the coordinates of m, n, m, and n.

Explanation:

Step1: Choose a Correct Statement (e.g., \( k = 1 \), so \( M'N' = MN \))

Let’s pick \( k = 1 \) (scaling factor 1 means no change). Choose \( M = (0, 5) \), \( N = (5, 5) \). Then \( MN \) length is \( 5 - 0 = 5 \) (horizontal line, same y - coordinate).

Step2: Find \( M' \) and \( N' \) for \( k = 1 \)

For \( k = 1 \), scaling (or transformation) leaves points unchanged. So \( M' = M = (0, 5) \), \( N' = N = (5, 5) \).

Step3: Label on the Graph

On the coordinate plane (with x - axis 0 - 15, y - axis including 5), mark \( M(0, 5) \), \( N(5, 5) \), \( M'(0, 5) \), \( N'(5, 5) \). The length \( MN = 5 \), \( M'N' = 5 \), so \( M'N' = MN \) (matches \( k = 1 \) statement).

Answer:

• \( k = 1 \)
• \( M = (0, 5) \), \( N = (5, 5) \), \( M' = (0, 5) \), \( N' = (5, 5) \) (Labels: \( M \) at (0,5), \( N \) at (5,5), \( M' \) at (0,5), \( N' \) at (5,5) on the graph)