Maths question class 10(coordinates geometry)

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

For the unknown point D there are 3 possibilities, but because it is called ABCD I assume it is between A and C. So

|DC| // |AB| which means,

d_x - c_x = a_x - b_x

d_x-(-6) = -3-(-1) = -2

d_x = -8

and

d_y - c_y = a_y - b_y

d_y - 2 = -4-(-3) = -1

d_y = 1

So D is (-8, 1)

Answer 2

I am not sure how to tell you to do this using the distance formula.

What I would do is this:

First calculate the equation of the line AB and call the slope m₁.

Then calculate the equation of the line BC and call the slope m₂.

Calculate the equation of the line with slope m₁ through the point C.

Then calculate the equation of the line with slope m₂ through the point A.

The intersection of these 2 equations is your required point.

Answer 3

Point D is located relative point C(-6, 2) similarly as point A(-3, -4) relative to point B(-1, -3). Point A is -2 along Ox and -1 along Oy from point B. Hence point D is -2 along Ox and -1 along Oy from point C(-6, 2). Hence point D is (-6 -2, 2 -1) = (-8, 1).