Coordinate Plane and Area

1. a) The points form a rectangle. Opposite sides are horizontal or vertical.

b) Horizontal side length:

From $x = -4$ to $x = 2$:

$2 - (-4) = 6$

Vertical side length:

$from y = -1 to y = 3$

$3 - (-1) = 4$

c) Area:

$A = 6 \times 4 = 24$

The area is 24 square units.

2. a) Segment PQ is horizontal, so it can be used as the base.

Base length:

$5 - (-3) = 8$

b) The height is the vertical distance from R to line PQ:

$6 - 1 = 5$

c) Triangle area:

$A = 1/2 \times base \times height$

$A = 1/2 \times 8 \times 5$

$A = 20$

The area is 20 square units.

3. a) The y-coordinates are the same, so find the horizontal distance:

$1 - (-7) = 8$

The distance is 8 units.

b) The x-coordinates are the same, so find the vertical distance:

$2 - (-5) = 7$

The distance is 7 units.

c) The x-coordinates are the same:

$-1 - (-6) = 5$

The distance is 5 units.

4. Find each rectangle area.

Rectangle A:

$8 \times 5 = 40$

Rectangle B:

$3 \times 4 = 12$

Add the areas:

$40 + 12 = 52$

The total area is 52 square meters.

5. a) Length:

$4 - (-6) = 10$

Width:

$3 - (-2) = 5$

Perimeter:

$P = 2 \times (10 + 5)$

$P = 30$

The perimeter is 30 units.

b) Area:

$A = 10 \times 5 = 50$

The area is 50 square units.

c) Side lengths are distances. A distance is how far apart two positions are, so it is positive. Subtracting coordinates such as $4 - (-6)$ gives the positive distance between them.