In the rectangular coordinate system, a line passes through the points (0, 5) and (7, 0)...

AAPL wrote: ↑

Thu Mar 19, 2020 1:41 am

Manhattan Prep

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)

OA D

Here's a quick 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

AAPL wrote: ↑

Thu Mar 19, 2020 1:41 am

Manhattan Prep

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)

OA D

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