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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)#.

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.

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Answer 2

Mason Adams

One other point that the second line may pass through if it is parallel to the first line is (2, 5).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.