Question

Line j passes through points (10, 7) and (3, 2). Line k passes through points (10, 10) and (3, 5). Are line j and line k parallel or perpendicular?

Parallel, perpendicular, neither?

Answer 1

Parallel

Explanation:

In order to find out if two lines or parallel, perpendicular, or neither, we must first find the slope between the two lines and then compare them.

Lets take our line j first.

We can use the formula
`(y_2-y_1)/(x_2-x_1)` and then plug in our coordinates to evaluate.

`(2-7)/(3-10)`

Evaluate. A negative divided by a negative is a positive.

`(-5)/(-7)=(5)/(7)`

Now lets do line k.

`(5-10)/(3-10)`

Evaluate

`(-5)/(-7) =(5)/(7)`

Now, to find out if a line is parallel or perpendicular we must first define what they mean in terms of slope.

Perpendicular: They form a right angle and they are the opposite reciprocal

Parallel: They are the same.

If we look at the slopes, we can conclude:

`(5)/(7)=(5)/(7)`

Therefore they are parallel.