Question

In the coordinate plane, three vertices of rectangle MNOP are M(0, 0), N(0, c), and P(d, 0). What are the coordinates of point O?. a.(d, c). b.(2d, 2c). c.(c/2, d/2). d.(c, d)

Answer 1

The coordinates of O is (d,c) .

Option (a) is correct .

Explanation:

As given

In the coordinate plane, three vertices of rectangle MNOP are M(0, 0), N(0, c), and P(d, 0).

As MNOP is a rectangle .

Thus opposite sides of the rectangles are equal .

Formula

`Distance\ formula = \sqrt{(x_(2)-x_(1))^(2)+(y_(2)-y_(1))^(2) }`

`NM = \sqrt{(0-0)^(2)+(c-0)^(2)}`

`NM = \sqrt{c^(2)}`

NM = c units

`MP = \sqrt{(d-0)^(2)+(0-0)^(2)}`

`MP = \sqrt{d^(2)}`

MP = d units

Thus the coordinate of the O (d,c) .

(This is because opposit sides of the rectangle are equal thus distance of point O from point P must be d and distance of point O from point N must be c .)

Therefore the coordinates of O is (d,c) .

Option (a) is correct .

Answer 2

MNOP is a rectangle.
In the coordinate plane, three vertices are: M ( 0, 0 ), N ( 0, c ) and P ( d, 0 ).
The coordinates of point O is:
A ) ( d, c )