Question

Two opposite vertices of a rectangle are (1, 3) and (5, 1) while the other two vertices lie on the the straight line y = 2x +

c. Then the value of c is

Answer 1

Solution:-

Let ABCD be a rectangle whose equal diagonals intersect at point O

Let, A=(1,3) and C=(5,1)

then, coordinates of midpoint O,

x=5+1/2

y=3+1/2. {from mid point formula}

Now, x=3 & y=2

It is given that other two vertices lie on a straight line, y=2x+c

Putting the value of x & y in the given eq. we get,

2=2×3+c

2=6+c

c=-4

Hence, solved