Question

A line passes through `(6 ,2 )` and `(1 ,3 )`. A second line passes through `( 7, 4 )`. What is one other point that the second line may pass through if it is parallel to the first line?

Answer 1

The second line could pass through point `(2,5)`.

Explanation:

I find the easiest way to solve problems using points on a graph is to, well, graph it out.

As you can see above, I've graphed the three points — `(6,2),(1,3),(7,4)`— and labelled them `"A"`, `"B"`, and `"C"` respectively. I've also drawn a line through `"A"` and `"B"`.

The next step is to draw a perpendicular line that runs through `"C"`.

Here I've made another point, `"D"`, at `(2,5)`. You can also move point `"D"` across the line to find other points.

The program I use is called Geogebra, you can find it here, and it's fairly straightforward to use.