Question

12
name a point that is
a vertical distance of
6 units from point m
that is within the
same quadrant as
point m?
(-6, -4)
(-6, 2)
(-12, 2)
not here

Explanation:

Step1: Identify Point M's coordinates

From the graph, Point M is at $(-5, 2)$.

Step2: Confirm M's quadrant

Point $(-5, 2)$ is in Quadrant II (negative x, positive y).

Step3: Calculate vertical distance

Vertical distance uses y-values. We need a point with y-coordinate such that $|y - 2| = 6$. Solving:
$y - 2 = 6 \implies y=8$, or $y - 2 = -6 \implies y=-4$.

Step4: Match quadrant and options

A valid point must be in Quadrant II (x negative, y positive/negative? No: Quadrant II is x negative, y positive. Wait, $y=-4$ would be Quadrant III, so only $y=8$ is Quadrant II, but check options:
Check $(-6, -4)$: Quadrant III, vertical distance $| -4 - 2 | = 6$, but wrong quadrant.
Check $(-6, 2)$: vertical distance $|2-2|=0$, not 6.
Check $(-12, 2)$: vertical distance $|2-2|=0$, not 6.

Answer:

not here