Question

The line through the midpoint of and perpendicular to the segment joining points (1, 0) and (5, -2).

Answer 1

What about that line? you need its equation?

Answer 2

What is the question

Answer 3

Yes please

Answer 4

You need to do a few steps to find it.
You can find the equation of a line if you know the slope of the line and one point on the line. Ok, so far?

Answer 5

What I did was take the slope and flip it to make -5/3 so it would be perpendicular. This was my first step, I'm hoping it was right.

Answer 6

Your idea is correct. Let's see if you got the slope correct.

Answer 7

I thought it was -5/3.......

Answer 8

How did you find the slope of the given segment?

Answer 9

Ummm.... Good question lol I just assumed because I was trying to find a perpendicular line and the original slope was 3/5 that it would be flipped to make -5/3. I'm getting the idea that this wasn't right.

Answer 10

Points: (1, 0) and (5, -2)
Slope of given segment:

\(m = \dfrac{-2 - 0}{5 - 1} = \dfrac{-2}{4} = -\dfrac{1}{2}\)

Now the slope of the perpendicular is the negative reciprocal, so you flip this slope and change the sign.

new slope \(= \dfrac{2}{1} = 2\)

The slope you need is 2.

Now you need one point the line goes through. You are told it goes through the midpoint of the given segment.
Do you know how to find the midpoint of a segment?

Answer 11

I believe its 1/2 (1 + 5), that would equal 3 for x and 1/2 (0+-2) and that would equal -1. Is that right?

Answer 12

I think I've got the answer now. Would it be: 2X + Y = 5

Answer 13

Ok, let's continue.
We have a new slope of 2.
Now we need a point. We use the midpoint of the segment.
\(M \left(\dfrac{1 + 5}{2}, \dfrac{0 - 2}{2}\right) = M(3, -1)\)

Yes, your midpoint is correct.

Answer 14

Now we need the equationj of a line with slope = 2, and going through point (3, -1)

We can use the slope-intercept form and solve for b.

y = mx + b
-1 = 2(3) + b
-1 = 6 + b
b = -7

Equation of the line is:

y = 2x - 7

In standard form:

2x - y = 7