Question

5. If the points P(5, 3) Q(-3, 3) R(-3, -4) and S form a rectangle, then find the coordinate of S.
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Answer 1

The coordinate of S. = ( 5 , - 4)  If the points P(5, 3) Q(-3, 3) R(-3, -4) and S form a rectangle,

Step-by-step explanation:

Let Say S coordinates = ( x , y)

PQRS is rectangle

slope of RS = Slope of PQ

=> ( y - (-4))/(x - (-3)  = (3 - 3)/(5 -(-3))

=>  ( y +4)/(x - 5)  = 0

=> y  = -4

PS = QR

=> (-4 - 3)² + ( x - 5)² =  (-3 - (-3))² + (3 - (-4))²

=> (7)² + (x - 5)² =  7²

=> x - 5  = 0

=> x =  5

( 5 , - 4)

the coordinate of S. = ( 5 , - 4)

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Answer 2

The coordinates of S is at (5,-4).

Step-by-step explanation:

When P(5,3),Q(-3,3),R(-3,-4) and S form a rectangle .

We know that

Opposite sides of rectangle are equal.

Therefor, PS=QR, RS=PQ

Distance formula between two points ($x_1,y_1)$ and ($x_2,y_2)$ is given by

Distance=$\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Using the formula

Length of QR=$\sqrt{(-3+3)^2+(-4-3)^2}$

Because distance is always positive.

Let coordinates of S is (x,y).

Length of PS=$\sqrt{(x-5)^2+(y-3)^2}$

Substitute

$\sqrt{(x-5)^2+(y-3)^2}=\sqrt{(-3+3)^2+(-4-3)^2}$

Squaring on both sides then we get

$(x-5)^2+(y-3)^2=(-3+3)^2+(-7)^2$

On comparing both sides then we get

$(x-5)^2=0$

$x-5=0$

$x=5$

$(y-3)^2=(-7)^2=49$

$y-3=\sqrt{49}=\pm 7$

Substitute y-3=7

Then, we get

y=7+3=10

Substitute y-3=-7

$y=-7+3=-4$

y= 10 is not possible if we take y=10 then the four point do not make rectangle.

It is clear from attached figure.

Therefore, the coordinates of S is at (5,-4).

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https://brainly.in/question/80270:Answered by Poojan