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?

1 Answer
sophie
Apr 25, 2018

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.

geogebra.org

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"#.

geogebra.org

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.

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