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A line segment containing the point (0,0) and (12,8) will

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by Vincen » Sun May 06, 2018 9:19 am
Hello M7MBA.

One way is to find the equation of the line. To find it we will use the following formula: $$y-y_0=\frac{y_1-y_0}{x_1-x_0}\left(x-x_0\right)$$ Let's call $$\left(x_0,y_0\right)=\left(0,0\right)\ and\ \ \ \left(x_1,y_1\right)=\left(12,8\right).$$ Then we get: $$y-0=\frac{8-0}{12-0}\left(x-0\right)$$ $$\Rightarrow\ \ y=\frac{2}{3}x\ .$$ Now, we have to substitute the coordinates of each point in the last equation: $$(A)\ \ (2,3)\ \ \ \Rightarrow\ \ \ 3=\frac{2}{3}\cdot2\ \ \Rightarrow\ \ 9=4\ \ \ \ false.$$ $$(B)\ \ (2,4)\ \Rightarrow\ \ \ 4=\frac{2}{3}\cdot2\ \ \Rightarrow\ \ 12=4\ \ \ \ false.$$ $$(C)\ \ (3,2)\ \Rightarrow\ \ \ 2=\frac{2}{3}\cdot3\ \ \Rightarrow\ \ 2=2\ \ \ \ Correct.$$ Therefore, the correct answer is the option [spoiler] C = (3 , 2) [/spoiler].

I hope it helps you.
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by Scott@TargetTestPrep » Tue May 08, 2018 3:16 pm
M7MBA wrote:A line segment containing the point (0,0) and (12,8) will also contain the point

(A) (2,3)
(B) (2,4)
(C) (3,2)
(D) (3,4)
(E) (4,2)
The slope of the line segment is (8 - 0)/(12 - 0) = 8/12 = 2/3. The equation of the line segment is:

y = (2/3)x + b

Substituting (0,0) we can determine b and we have:

b = 0

So the equation of the line segment is:

y = (2/3)x

We see that if x = 3, then y = 2. Thus (3, 2) is a point on the line segment.

Answer: C

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by [email protected] » Tue May 08, 2018 4:53 pm
Hi M7MBA,

We're told that a line segment contains the point (0,0) and (12,8). We're asked which of the 5 points will also be on that line. Since we're dealing with 'line rules', we can use the relationship between the 2 points that we're given - and the design of the answer choices - to get the correct answer without too much trouble.

To start, since (0,0) and (12,8) are on the line, we know that the slopes is LESS than +1 (since the increase in the X-coordinate is greater than the increase in the Y-coordinate). By extension, all of the 'positive co-ordinate points' on this line will have an X that is greater than the Y. Eliminate Answers A, B and D.

Next, with the remaining two answers (3,2) and (4,2), we can see that the first co-ordinate matches the pattern from (12,8) - they both are in the ratio of 3:2 relative to the other co-ordinate at (0,0), so Answer C must be the answer.

Final Answer: C

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