Question

If two rectangles ABCD and PQRS whose sides are parallel to the coordinate axes are drawn as shown in below figure then the coordinates of 'Q' is ___

• A. (10,-4)
• B. (-4, 10)
• C. (10, 4)
• D. (4, 10)

Answer 1

The correct option is A

(10,-4)

Given B = (5,6)

Let E, F, G, H be the intersection points of these two rectangles.

Now AE = BF = 6 cm ($\because$ Opposite sides in a rectangle are equal)

$\therefore$ y-coordinate F = y-coordinate of B - 6

= 6 - 6

= 0

and x-coordinate of F = x-coordinate of B ($\because$ BF is parallel to Y-axis)

$\therefore$ F = (5,0)

Given FR = 5 cm

$\because$ FR is parallel to X-axis, y-coordinate of F = y-coordinate of R

and x-coordinate R = x-coordinate of R + 5

= 5 + 5

= 10

$\therefore$ R = (10,0)

PS = RQ = 4 cm ($\because$ Opposite sides in a rectangle are equal)

$\therefore$ y-coordinate Q = y-coordinate of R - 4

= 0 - 4

= -4

and x-coordinate of Q = x-coordinate of R ($\because$ RQ is parallel to Y-axis)

$\therefore$ Q = (10,-4)