Question

A(1,3) and C(5,1) are 2 opposite vertices of rectangle ABCD. If the slope of line BD is 2, then the equation of BD is?

Answer 1

For line BD, slope is 2.i.e m = 2

Let equation of BD be y = mx + c
or y = 2x + c

We have to find the value of c.

The diagonals of a rectangle intersect at a point. This point is the midpoint of both the diagonals and let that be (h,k)

So, h = (1 + 5)/2 = 3
k = (3 + 1)/2 = 2

So the common point is (3,2) and this point also satisfies the equation of BD i.e y = 2x + c

Now putting (3,2) in y = 2x + c
2 = 2(3) + c
c = - 4

Now, the required equation of BD is
y = 2x - 4 or
2x - y - 4 = 0

Hope This Helps You!

Answer 2

We know that, The diagonals of a rectangle intersects at a point.

Now, Here the diagonals are AC,BD

We know that mid point of any diagonal is the intersection point.

Now, The intersection point is (1+5/2),(3+1/2) = (3,2)

We know that any point on the line, is a solution of the line and vice - versa.

Hence, (3,2) is a solution of line BD.

Given slope of BD, m= 2

We know that general form of a line with slope m is y = mx + c

Now, taking y =2, x =3

2 =2(3)+c

2 =6+c

c =-4

So,

The equation of the line is y = 2x -4 or 2x-y -4 =0