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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:.aPoints R and S are to the left of Points P and Q.bPoints R and S are to the right of Points P and Q

Sagot :

Mhanifaidn

Answer:

  • See below

Step-by-step explanation:

Given points P and Q have same x-coordinate but different y- coordinates.

The distance between P and Q is the difference of y- coordinates:

  • PQ = 4 - (-4) = 8 units = 8 cm

The area is 64 cm², it means the adjacent sides are

  • PS = QR = 64/8 = 8 cm

a)

If the points R and S are to the left, their coordinates are

  • S = (-1 - 8, 4- 0) = (- 9, 4)
  • R = (-1 - 8, - 4 - 0) = (- 9, -4)

b)

If the points R and S are to the right, their coordinates are

  • S = (-1 + 8, 4 + 0) = (7, 4)
  • R = (-1 + 8, - 4 + 0) = (7, -4)
Semsee45idn

Answer:

Points R and S are to the left of Points P and Q

R = (-9, 4)

S = (-9, -4)

Points R and S are to the right of Points P and Q

R = (7, 4)

S = (7, -4)

Step-by-step explanation:

Given coordinates:

  • P = (-1, 4)
  • Q = (-1, -4)

Points P and Q have the same x-value.

The vertical distance between these two points is:

[tex]\begin{aligned}\implies \sf y_P-y_Q & =\sf 4-(-4)\\ & =\sf 4+4\\ & =\sf 8\:units \\ & =\sf 8\:cm\end{aligned}[/tex]

Area of a rectangle = width × length

If the area of the rectangle PQRS is 64 cm² then:

[tex]\begin{aligned} \implies \sf 64 & = \sf width \times 8\\\implies \sf width & = \sf \dfrac{64}{8}\\\implies \sf width& = \sf 8 \: cm \end{aligned}[/tex]

This means that the y-values of points R and S will be the same as points P and Q, but the x-values will either be 8 less or 8 more.

Points R and S are to the left of Points P and Q

R = (-1 - 8, 4) = (-9, 4)

S = (-1 - 8, -4) = (-9, -4)

Points R and S are to the right of Points P and Q

R = (-1 + 8, 4) = (7, 4)

S = (-1 + 8, -4) = (7, -4)

View image Semsee45
View image Semsee45
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