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Point A ( 4, 6) lies on a line with slope
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10 Mar 2019, 10:28

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Point A ( 4, 6) lies on a line with slope \(- \frac{3}{4}\) Point B lies on the same line and is 5 units from Point A. Which of the following could be the coordinates of Point B?

Indicate all such coordinates.

A. (− 1, 1)

B. (− 4, 12)

C. (8, 3)

D. (1, 10)

E. (0, 9)

Indicate all such coordinates.

A. (− 1, 1)

B. (− 4, 12)

C. (8, 3)

D. (1, 10)

E. (0, 9)

Re: Point A ( 4, 6) lies on a line with slope
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16 Mar 2019, 05:31

1

how C is also the correct choice, pls explain. I got only E as the right answer

Re: Point A ( 4, 6) lies on a line with slope
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16 Mar 2019, 17:16

Expert Reply

You can also move vertically − 3 and horizontally 4 to point (4 + 4, 6 − 3) = (8, 3), which lies on the same line. This distance from point A to the new point (8, 3) is also 5.

C and E are the answers.

Regards

C and E are the answers.

Regards

Re: Point A ( 4, 6) lies on a line with slope
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19 Jun 2019, 07:47

Carcass wrote:

You can also move vertically − 3 and horizontally 4 to point (4 + 4, 6 − 3) = (8, 3), which lies on the same line. This distance from point A to the new point (8, 3) is also 5.

C and E are the answers.

Regards

C and E are the answers.

Regards

I got the math correct by using few calculations ( or right triangles and then mid point). But it took much time.

Is their any GRE-way to save time in such case?

Thank you.

Re: Point A ( 4, 6) lies on a line with slope
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19 Jun 2019, 11:27

Expert Reply

I think no. Above is the fastest solution that I know.

Maybe there is another approach. Maybe @GreenLightTestPrep could come in handy...............

Maybe there is another approach. Maybe @GreenLightTestPrep could come in handy...............

Re: Point A ( 4, 6) lies on a line with slope
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27 Jun 2019, 16:24

Carcass wrote:

You can also move vertically − 3 and horizontally 4 to point (4 + 4, 6 − 3) = (8, 3), which lies on the same line. This distance from point A to the new point (8, 3) is also 5.

C and E are the answers.

Regards

C and E are the answers.

Regards

But how point (8, 3) could lie in a same line while we may calculate this line's equation which is y = - 3/4 * x + 9?

Only points B and E lie there!

Re: Point A ( 4, 6) lies on a line with slope
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29 Jun 2019, 02:19

Carcass wrote:

C and E are the answers.

Regards

what of point (1,10)

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Re: Point A ( 4, 6) lies on a line with slope
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29 Jun 2019, 05:38

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Carcass wrote:

Point A ( 4, 6) lies on a line with slope \(- \frac{3}{4}\) Point B lies on the same line and is 5 units from Point A. Which of the following could be the coordinates of Point B?

Indicate all such coordinates.

A. (− 1, 1)

B. (− 4, 12)

C. (8, 3)

D. (1, 10)

E. (0, 9)

Indicate all such coordinates.

A. (− 1, 1)

B. (− 4, 12)

C. (8, 3)

D. (1, 10)

E. (0, 9)

First sketch the given information:

Attachment:

Point A ( 4, 6) lies on a line with slope-1.png [ 8.38 KiB | Viewed 7371 times ]

Since the slope (rise/run) of the line is -3/4, for every 3 units we move UP, we move 4 units to the LEFT (alternatively, we can say for every 3 units we move DOWN, we move 4 units to the RIGHT)

Attachment:

Point A ( 4, 6) lies on a line with slope-2.png [ 10.91 KiB | Viewed 7355 times ]

Notice that we end up with a RIGHT triangle with legs of length 3 and 4, which means the hypotenuse must be length 5.

So, the point (0, 9) is on the line AND it is 5 units from the point (4, 6)

Likewise, if we start from (4, 6) and move 3 units DOWN, and 4 units to the RIGHT, we get the following:

Attachment:

Point A ( 4, 6) lies on a line with slope-3.png [ 10.9 KiB | Viewed 7316 times ]

Once again, we end up with a RIGHT triangle with legs of length 3 and 4, which means the hypotenuse must be length 5.

So, the point (8, 3) is on the line AND it is 5 units from the point (4, 6)

Answer: C, E

Cheers,

Brent

Retired Moderator

Joined: **10 Apr 2015 **

Posts: **6218**

Given Kudos: **136 **

Re: Point A ( 4, 6) lies on a line with slope
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29 Jun 2019, 05:40

dare90 wrote:

Carcass wrote:

C and E are the answers.

Regards

what of point (1,10)

The point (1, 10) is, indeed, 5 units from (4, 6). However, (1, 10) does not lie ON the given line.

Cheers,

Brent

Retired Moderator

Joined: **16 Apr 2020 **

Status:**Founder & Quant Trainer**

Affiliations: **Prepster Education**

Posts: **1546**

Given Kudos: **172 **

Location: **India**

WE:**Education (Education)**

Point A ( 4, 6) lies on a line with slope
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14 Mar 2021, 21:57

Carcass wrote:

Point A ( 4, 6) lies on a line with slope \(- \frac{3}{4}\) Point B lies on the same line and is 5 units from Point A. Which of the following could be the coordinates of Point B?

Indicate all such coordinates.

A. (− 1, 1)

B. (− 4, 12)

C. (8, 3)

D. (1, 10)

E. (0, 9)

Indicate all such coordinates.

A. (− 1, 1)

B. (− 4, 12)

C. (8, 3)

D. (1, 10)

E. (0, 9)

A = (4, 6)

B = (x, y)

Since, they both lie on the same line, they must have same slope as \(\frac{-3}{4}\)

A. slope = \(\frac{(6 - 1)}{(4 + 1)} = 1\)

B. slope = \(\frac{(6 - 12)}{(4 + 4)} = \frac{-3}{4}\)

C. slope = \(\frac{(6 - 3)}{(4 - 8)} = \frac{-3}{4}\)

D. slope = \(\frac{(6 - 10)}{(4 - 1)} = \frac{-4}{3}\)

E. slope = \(\frac{(6 - 9)}{(4 - 0)} = \frac{-3}{4}\)

Now, lets check the distance!

B. \((6 - 12)^2 + (4 + 4)^2 ≠ 5^2\)

C. \((6 - 3)^2 + (4 - 8)^2 = 5^2\)

E. \((6 - 9)^2 + (4 - 0)^2 = 5^2\)

Hence. option C and E

Re: Point A ( 4, 6) lies on a line with slope
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12 Jul 2024, 15:04

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Re: Point A ( 4, 6) lies on a line with slope [#permalink]

12 Jul 2024, 15:04
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