Coordinates and graphs (four quadrants)

Advanced Math 6 · Unit 10 · four-quadrant-plane · Teacher edition

four-quadrant-plane

Name ______________________________Date ______________

1.
In which quadrant is the point $(-3, 4)$ ?
1. (A)
  Quadrant I
2. (B)
  Quadrant II
3. (C)
  Quadrant III
4. (D)
  Quadrant IV
2.
What is the distance between the points $(2, 5)$ and $(2, -1)$ ?
Answer: ______________
3.
A rectangle has vertices $(-3, 2)$ , $(4, 2)$ , $(4, -1)$ , and $(-3, -1)$ . What is its perimeter?
Answer: ______________
4.
Which point lies on the line $y = 2x - 1$ ?
1. (A)
  $(1, 2)$
2. (B)
  $(2, 3)$
3. (C)
  $(0, 1)$
4. (D)
  $(-1, -2)$
5.
A triangle has vertices $(-2, 1)$ , $(4, 1)$ , and $(4, 5)$ . What is its area?
Answer: ______________

Answer key — Coordinates and graphs (four quadrants)

1.
(B)
Quadrant II
four-quadrant-plane-01
Negative $x$ , positive $y$ is the upper left: Quadrant II. (Quadrant III is lower left, where both are negative.)
2.
6four-quadrant-plane-02
$\lvert 5 - (-1) \rvert = \lvert 6 \rvert = \mathbf{6}$ . The common mistake is $5 - 1 = 4$ , ignoring that $-1$ is on the other side of the axis.
3.
20four-quadrant-plane-03
Width $7$ , height $3$ : $P = 2(7 + 3) = \mathbf{20}$ .
4.
(B)
$(2, 3)$
four-quadrant-plane-04
$x = 2$ gives $y = 3$ , so $\mathbf{(2, 3)}$ is on the line. Checks: $(0,1)$ gives $-1 \ne 1$ ; $(-1,-2)$ gives $-3 \ne -2$ .
5.
12four-quadrant-plane-05
$A = \frac{1}{2} \cdot 6 \cdot 4 = \mathbf{12}$ square units.