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# A, B, C, and D are four points on the same straight line....

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A, B, C, and D are four points on the same straight line.... [#permalink]  15 Dec 2017, 10:10
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A, B, C, and D are four points on the same straight line. The distances between the successive points are equal. If A is (1, -3), C is (4, a), and D is (b, 5). Find the values of a and b.

<----A(1, -3)----B----C(4, a)----D(b, 5)---->

How do I solve this question and what are the answers of a and b?

Source: HAESE MATHEMATICS Mathematics for the international student 10E MYP 5 (extended)
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Joined: 07 Jun 2014
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GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
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Re: A, B, C, and D are four points on the same straight line.... [#permalink]  15 Dec 2017, 11:18
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A, B, C, and D are four points on the same straight line. The distances between the successive points are equal. If A is (1, -3), C is (4, a), and D is (b, 5). Find the values of a and b.

<----A(1, -3)----B----C(4, a)----D(b, 5)---->

How do I solve this question and what are the answers of a and b?

Source: HAESE MATHEMATICS Mathematics for the international student 10E MYP 5 (extended)

Hello,

We explicitly solve GRE questions on this forum. And this is not one or at the very least not formattted like one.

That being said,

You have two variables a and b. among the points. Now since they are on the same line so you can write equations for slope

Slope AC = Slope AD = $$\frac{a+3}{3}=\frac{8}{b}$$.

Also points are equidistant AB = BC = CD.

So you can write something line AC=2 * CD. So distance equation gives the second equation.

Solve then for a and b.

Regards,
Sandy
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Sandy
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Re: A, B, C, and D are four points on the same straight line....   [#permalink] 15 Dec 2017, 11:18
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