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In a rectangular coordinate system ,which of the following points is intersected by the line connected by the coordinates (5,6) and(21,18)? A.(9,9) B.(12,12) C.(13,13) D.(12,13) E.(16,15)

The slope of a line passing through the points (5,6) and (21,18) is "rise over run": \(\frac{18-6}{21-5}=\frac{3}{4}\).

The slope of a line passing through the point (5,6) and one of the points from the answer choice must also be \(\frac{3}{4}\) (as it's the same lin), so \(\frac{y-6}{x-5}=\frac{3}{4}\).

Answer choice A works: \(\frac{9-6}{9-5}=\frac{3}{4}\).

Re: In a rectangular coordinate system ............ [#permalink]

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20 Oct 2010, 03:15

pzazz12 wrote:

In a rectangular coordinate system ,which of the following points is intersected by the line connected by the coordinates (5,6) and(21,18)? A.(9,9) B.(12,12) C.(13,13) D.(12,13) E.(16,15)

Equation of the line connecting the two points,(5,6) and (21,18);

y-6= {(6-18)/(5-21)}(x-5) or , 4y-3x=9

Only ( 9,9) is satisfying the equation.Hence answer is A.

In a rectangular coordinate system, which of the following [#permalink]

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31 Dec 2014, 10:24

1

This post received KUDOS

I found the equation of the line to be \(y = \frac{3x}{4} + \frac{9}{4}.\). Then, noticing that 3 of the options had the same value for x and y, I wanted to check at which point on the line the x and y values were equal. So I solved for x:

Therefore, (9,9) is a point on the line and our answer is A.

Further: If we would have found some other value (one that wasn't listed on the answer choices) then we at least could have eliminated 3 of the answer choices and then manually checked the other two.