Question

The three vertices of a parallelogram ABCD taken in order are A(3, -4), B(-1, -3) and C(-6, 2). Find the coordinates of the fourth vertex D using distance formula

Answer 1

Answer:

It's simple. Since it is a parallelogram, the opposite sides are congruent. So assume the coordinates of D to be (x, y).

As per the given data we can plot the three points A, B and C and join them. Using distance formula we can get BC and AB.

The formula is

Distance = sqrt{ (x1 - x2) ^2 + (y1 - y2) ^2) }

Now that we have the exact values, we can use it to find the coordinates of D by equating it with the distance equation for the opposite side ie.

AB = CD & BC = AD.

{Remember to substitute x and y in place of x2 and y2}

Now we have two equations with two variables. Use any method you feel convenient to get the coordinates of D.