Question

week 1 - mr mccray math check
coordinate plane & gra

1. which point is in quadrant ii?

a) (4, 3) b) (-5, 2) c) (-3, -2) d) (0, 4)

1. the distance between (2, 5) and (2, -1) is

a) 3 b) 4 c) 5 d) 6

1. true/false: points (x, y) and (x, -y) are re

Explanation:

Step1: Recall quadrant rules

In the coordinate - plane, Quadrant II has points with negative x - coordinates and positive y - coordinates.
For point A) $(4,3)$, $x = 4>0$ and $y = 3>0$, so it is in Quadrant I.
For point B) $(-5,2)$, $x=-5 < 0$ and $y = 2>0$, so it is in Quadrant II.
For point C) $(-3,-2)$, $x=-3 < 0$ and $y=-2 < 0$, so it is in Quadrant III.
For point D) $(0,4)$, $x = 0$ and $y = 4>0$, so it is on the y - axis.

Step2: Calculate distance between points

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. Here, $x_1 = 2,y_1 = 5,x_2 = 2,y_2=-1$.
Since $x_1=x_2 = 2$, the distance $d=\vert y_2 - y_1\vert=\vert-1 - 5\vert=\vert-6\vert = 6$.

Step3: Analyze point reflection

The points $(x,y)$ and $(x, - y)$ are reflections of each other across the x - axis.

Answer:

1. B. $(-5,2)$
2. D. 6
3. True (points $(x,y)$ and $(x, - y)$ are reflections across the x - axis)