Question

QP contains the points Q(-6,10) and P(-12,-2). Find the slope of a line perpendicular to QP

Answer 1

Answer: -2

Step-by-step explanation: Find the slope of between the two points. P is the bottom point and Q is the top point. Both x and y numbers increase, meaning that the slope is positive. The x numbers increase by 6, and the y numbers increase by 12. This means that the rise is 12, and the run is 6. The slope is 12/6 but can be simplified to 2/1. The perpendicular slope is -1/2 because the perpendicular slope of a line is opposite reciprocal. This means to make the number negative and to flip it.

Answer 2

-1/2

Explanation:

So we are asked to find the slope of a line perpendicular to the line going through Q(-6,10) and P(-12,-2).

To do this we first need to find the slope of the line going through Q(-6,10) and P(-12,-2).

We can use the slope formula for a line given two points on that line which is (y2-y1)/(x2-x1).

I like to do something I consider easier to remember and is the same thing

It is:

A) line up the points

B) subtract vertically

C) put 2nd difference over first difference

D) done unless it needs reducing

So that is exactly what I'm going to do here:

(-6, 10)

-(-12,-2)

------------

6 12

So the slope is 12/6 or 2.

Now you might prefer to write 2 as a fraction now, because I'm about to tell you to find the slope of a line that is perpendicular, you just need to take the opposite reciprocal.

Opposite means to change the sign. I'm referring to negative or positive sign.

Reciprocal means to flip the number.

Let's put 2 through that process.

Opposite of 2: -2

Reciprocal of the opposite: -1/2

I got that reciprocal there by realizing -2 is just -2/1.

Anyways the slope of a line that is perpendicular to the one that goes through P and Q is -1/2 or -0.5.