Points A(1, 1), B(−1, 0), and C(0, 1) are given. Find point D(x , y ), such that vectors AB and CD are equal.

Question

Points A(1, 1), B(−1, 0), and C(0, 1) are given. Find point D(x , y ), such that vectors AB and CD are equal.

Answer 1

Hi, Sada!

Vector AB [(1, 1) to ( -1, 0)] and Vector CD [(0, 1) to (x, y)] need to be equal to each other. This means that the distance between A and B needs to be equal to the distance between C and D.

Let's start with x values!

We know that the x value of A is 1, and that the x value of B is -1. From the starting point, 1, we need to move -2 units to get to -1, which is the ending point.

We also know that the x value of C is 0. Since we moved -2 units to get from A's x-value to B's x-value, let's do the same for C's x-value to D's x-value. If we move -2 units from 0, we get -2 as an ending point. This is D's x-value.

Let's move on to the y values!

We know that the y-value of A is 1, and the y-value of B is 0. From starting point A to ending point B (to get from 1 to 0), we move -1 units.

We also know that the y-value of C is 1. We need to move -1 units from 1 to reach ending point D. We're left with 0 for D's y-value.

All that's left to do from here is to plug those x and y values into the point (x, y) for D. You can always check your work afterward by plotting all the points on graph paper, drawing lines AB and CD, and then counting to make sure the horizontal and vertical distances are equal to each other.

Hope this helps!