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Rectangle PQRS is plotted on a coordinate plane. The coordinates of P are

(-1, 4) and the coordinates of Q are (-1,-4). Each unit on the coordinate
plane represents 1 centimeter, and the area of rectangle PQRS is 64 square
centimeters. Find the coordinates of points R and S given these conditions:
a)
Points R and S are to the left of points P and Q.
b) Points R and S are to the right of points P and Q.
PLS HELP ITS DUE TOMORROW

User Esteam
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1 Answer

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Answer: 8 * 8 = (distance between PQ and RS) * 8

distance between PQ and RS = 8" PQRS in units: 16 because 8 (PQ) + 8 (RS)=16, measurement type is units so 16 units

Step-by-step explanation:

*I used A.I to help explain this better.* It should make sense, just read/scan through it, as it explains the question very throughly.

"First, let's find the length of the sides of the rectangle. Since P and Q have the same x-coordinate, we know that PQ is a vertical line segment with length 8 units (since the y-coordinates of P and Q differ by 8). Similarly, since P and Q have the same y-coordinate, we know that RS is a horizontal line segment with length 8 units. Therefore, the length and width of the rectangle are both 8 units.

To find the coordinates of points R and S, we need to consider two cases:

a) Points R and S are to the left of points P and Q.

In this case, we can imagine that the rectangle is reflected across the y-axis, so that points P and Q become points P'(-1, -4) and Q'(-1, 4), respectively. Then, points R and S must lie on the line x=-2 (to the left of point P'), and the distance between them must be 8 units.

Since the area of the rectangle is 64 square centimeters, the length of RS is 8 units, and the length of PQ is 8 units, we know that the distance between PQ and RS (i.e., the height of the rectangle) is also 8 units. This means that the y-coordinates of R and S must differ by 8 units.

Let's choose a y-coordinate for point R. Since R is to the left of P', its x-coordinate is -2, and its y-coordinate must be between -4 and 4 (since the y-coordinates of P' and Q' are -4 and 4, respectively). Let's say that the y-coordinate of R is yR. Then, the y-coordinate of S must be yR + 8.

The area of the rectangle is (length)(width) = (8)(8) = 64 square centimeters. Since PQ is a vertical line segment, its length is the difference between the y-coordinates of P and Q, which is 8 units. Therefore, the length of RS is also 8 units. The distance between PQ and RS (i.e., the height of the rectangle) is also 8 units. Therefore, we can write:

8 * 8 = (distance between PQ and RS) * 8

distance between PQ and RS = 8

So, the y-coordinates of R and S differ by 8 units. Therefore, we can write:

yR + 8 - yR = 8

yR = 0

Therefore, the coordinates of R are (-2, 0), and the coordinates of S are (-2, 8).

b) Points R and S are to the right of points P and Q.

In this case, we can imagine that the rectangle is reflected across the x-axis, so that points P and Q become points P''(1, 4) and Q''(-1, 4), respectively. Then, points R and S must lie on the line y=-6 (to the right of point P''), and the distance between them must be 8 units.

Again, the area of the rectangle is (length)(width) = (8)(8) = 64 square centimeters. Since RS is a horizontal line segment, its length is the difference between the x-coordinates of R and S, which is 8 units. Therefore, the length of PQ is also 8 units. The distance between PQ and RS (i.e., the height of the rectangle) is also 8 units. Therefore, we can write:

8 * 8 = (distance between PQ and RS) * 8

distance between PQ and RS = 8"

User Cryn
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