In the rectangular coordinate system, a line passes through the points (0,5) and

BTGModeratorVI wrote: ↑

Thu Jun 18, 2020 5:42 am

In the rectangular coordinate system, a line passes through the points (0,5) and (7,0). Which of the following points must the line also pass through?

A)(-14, 10)

B)(-7, 5)

C)(12, -4)

D)(14, -5)

E)(21, -9)

Answer: D
Source: Manhattan prep

The point that lies on the lines joining the points (0,5) and (7,0) and one between the points (0,5) and (7,0) would have the same slope as that of the points (0,5) and (7,0).

So, let's first calculate the slope of the points (0,5) and (7,0).

m = slope = (0 – 5)/(7 – 5) = –5/2

Taking a point (0, 5), let's take each option one by one.

A)(-14, 10)

m = slope = (10 – 5)/(–14 – 0) = –5/14 ≠ –5/2. Not the correct answer.

B)(-7, 5)

m = slope = (5 – 5)/(–7 – 0) = 0 ≠ –5/2. Not the correct answer.

C)(12, -4)

m = slope = (–4 – 5)/(12 – 0) = –9/12 = –3/4 ≠ –5/2. Not the correct answer.

D)(14, -5)

m = slope = (–5 – 5)/(14 – 0) = –10/14 = – ≠ –5/2. Not the correct answer.

E)(21, -9)

m = slope = (–9 – 5)/(21 – 0) = –14/21 = –2/3 ≠ –5/2. Not the correct answer.

None of the above is the correct answer. Sees there's a typo.

Hope this helps!

-Jay
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BTGModeratorVI wrote: ↑

Thu Jun 18, 2020 5:42 am

In the rectangular coordinate system, a line passes through the points (0,5) and (7,0). Which of the following points must the line also pass through?

A)(-14, 10)

B)(-7, 5)

C)(12, -4)

D)(14, -5)

E)(21, -9)

Answer: D
Source: Manhattan prep

Here's another possible approach..

First plot of the two given points:


Notice that, to get from one point (0, 5) to the other point (7, 0), we must go down 5 units and then to the right 7 units


If we continue this pattern....

.... The next point on the line is at (14, -5)

Answer: D

Cheers,
Brent

BTGModeratorVI wrote: ↑

Thu Jun 18, 2020 5:42 am

In the rectangular coordinate system, a line passes through the points (0,5) and (7,0). Which of the following points must the line also pass through?

A)(-14, 10)

B)(-7, 5)

C)(12, -4)

D)(14, -5)

E)(21, -9)

Answer: D

Solution:

We see that the slope of the line is (0 - 5) / (7 - 0) = -5/7. Now let’s check each given answer choice by determining the slope between that point and (0, 5).

A. (10 - 5) / (-14 - 0) = 5/(-14) = -5/14 → This is not -5/7.

B. (5 - 5) / (-7 - 0) = 0/(-7) = 0 → This is not -5/7.

C. (-4 - 5) / (12 - 0) = -9/12 = -3/4 → This is not -5/7.

D. (-5 - 5) / (14 - 0) = -10/14 = -5/7 → This is -5/7.

Answer: D