ShmoopTube

00:02

Here's another shmoop du jour...

00:05

One endpoint of a line segment is (3, -4). If the midpoint is (2, 1), what is the other

00:12

endpoint? And here are your potential answers...

00:17

Ok so this question is asking us to basically apply the midpoint formula...

00:20

Okay... if we're given two points....x1, y1, and x2, y2...

00:24

...the midpoint between the two points can be found with the formula: x1 plus x2 divided

00:30

by 2, y1 plus y2 divided by 2. But we're not given the two endpoints. Instead,

00:37

we're given the midpoint and one other point...

00:40

Not a problem. Let's place these values in the midpoint formula.

00:44

(2,1) equals the quantity 3 plus x... divided by 2... and the quantity negative 4 plus y

00:50

divided by 2. So the x coordinate equation is 2 equals 3

00:56

plus x divided by 2...and the y coordinate is 1 equals negative 4 plus y divided by 2.

01:03

Now let's go to the x coordinate equation. Multiply both sides by 2...

01:07

So 4 equals 3 plus x. Then we subtract both sides by 3..

01:12

So the x coordinate is 1.

01:14

Well, now let's go to the y-coordinate equation.

01:17

Multiply both sides by 2. 2 equals negative 4 plus y. Add 4 to both sides...

01:22

So y equals 6. And yeah, it's answer choice E!

Full Transcript