Question

a rectangle pqrs the points p=(2,3) q=(X1,Y1) r=(8,11) s=X2,Y2) then the line qs is known to be parallel to the y axis then the coordinates of q and s are respectively,a)(0,7) b)(5,2) and (5,12) c) (7,6) and (7,10) d) none
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Answer 1

56 is your answer..........

Answer 2

Concept:

The rectangle is a 2D shape, having four sides and four angles, sum of all angles is 360° and the opposite sides are equal.

Given:

A rectangle PQRS the points P = (2,3),  Q = (X1,Y1),   R = (8,11),   S = (X2,Y2).

The line QS is parallel to the y-axis.

Find:  

We are asked to find out the coordinates of Q and S.

Solution:

Now,

As QS is parallel to the Y-axis,

Then,

X-coordinate of both Q and S will be the same.

So, we have to find the Y-coordinate.

Now,

(y₁ + y₂) / 2 = 7

⇒ (y₁ + y₂) = 14

Now,

[(y₁ - 3)/3] × [(y₁ - 11)/(-3)] = (-1)

(y₁ - 3) × (y₁ - 11) = 9

(y₁ )² - 11y₁ - 3y₁ + 33 = 9

(y₁ )² - 14y₁ + 33 = 9

(y₁ )² - 14y₁ + 24 = 0

NOw using mid term split method,

(y₁ )² - 12y₁ - 2y₁ + 24 = 0

NOw taking common,

y₁ (y₁ - 12) -2 (y₁ -12) = 0

(y₁ - 2) (y₁ - 12) = 0

We get,

(y₁ - 2) = 0

⇒ y₁ = 2

And,

(y₁ - 12) = 0

⇒ y₁ = 12

As mentioned above X-coordinate are the same and we have Y-coordinate 2 and 12.

Hence we can say that the coordinates of Q and S are (5,2) and (5,12).

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