Question Video: Finding the Unknown Coordinates of a Point Using the Midpoint Formula Mathematics • Third Year of Preparatory School

Video Transcript

The origin is the midpoint of the straight segment 𝐴𝐵. Find the coordinates of point 𝐵 if the coordinates of point 𝐴 are negative six, four.

First, we need to know where the origin is on a coordinate plane. The origin is point zero, zero. And the midpoint is located along a line halfway between the two endpoints. We find the midpoint by averaging the 𝑥-coordinates of the two endpoints and the 𝑦-coordinates of the two endpoints.

We have a midpoint at zero, zero. And we have an endpoint, point 𝐴, at negative six, four. And then, we have the unknown coordinates of the other endpoint, 𝐵. We’ll call it 𝑥, 𝑦. Since we know that the midpoint is zero, zero, we could create two equations to solve for our missing values. We’ll let 𝐴 be 𝑥 one, 𝑦 one and 𝐵 be 𝑥 two, 𝑦 two. So, we have negative six plus 𝑥 divided by two has to be equal to zero and positive four plus 𝑦 over two has to be equal to zero.

To make this value equal to zero, we need zero in the numerator. So, we need to say what plus negative six equals zero. If 𝑥 equals six, negative six plus six equals zero. And for the numerator in the 𝑦-coordinate, if 𝑦 is negative four, four plus negative four equals zero. And that means 𝐵 must be located at six, negative four.

We could’ve also used a graph to solve this problem. If the midpoint is at zero, zero and point 𝐴 is negative six, positive four, then to find the other endpoint, we need to do the opposite. We need to go right six, that’s positive six, and down four. This is because we know that the midpoint divides the line segment in half. And zero, zero is halfway between negative six, four and six, negative four. Both methods show the missing endpoint to be 𝐵: six, negative four.