Question

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

Answer 1

Answer:

(2√2,√7)

Step-by-step explanation:

Answer 2

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

Step-by-step explanation:

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

Let say S (x , y)

Length of PQ = Length of RS

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

=>  64 = x² + 9 + 6x  + y² + 16 + 8y

=> x² + y² + 6x + 8y  = 39   Eq1

Length of PS = Length of QR

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

=> x² + 25  - 10x + y² + 9 - 6y  = 49

=> x² + y²  - 10x - 6y = 15    Eq2

Eq1 - Eq2

=> 16x  + 14y  =  24

=> 8x + 7y = 12

PR  = QS

=> 8² + 7² = (x + 3)² + (y - 3)²

=> x² + y² + 6x - 6y = 95   Eq3

Eq1 - Eq3

=> 14y = -56

=> y = -4

8x + 7(-4) = 12

=> 8x = 40

=> x = 5

(5 , - 4) is coordinate of S

Learn More

Three vertices of a rectangle are A (1,3), B(1,-1), and C(7,-1)

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