Point A(4, 6) lies on a line with slope -3/4 Point B lies on the same

Question

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?

I. (8, 3) 
II. (1, 10) 
III. (0, 9)

A. I only
B. II only
C. III only
D. I and III only
E. I, II and III

LeoN88 · Answer

Line:-

y= (-3/4)x + c

Putting A(4, 6), c=9

y= (-3/4)x + 9, this is satisfied by both I and III

Also, I and III, these points are 5 units from A(4, 6) in distance.
 D. I and III only

firas92 · Answer

Alternatively,

We know that  slope = \frac{(y2-y1)}{(x2-x1)}

From the given slope, we can deduce that

If x coordinate changes by 4 units, y coordinate must change by -3 units, or

If, x coordinate changes by -4 units, y coordinate must change by 3 units

Only I and III satisfy and they are both 5 units away from (4,6)

Answer is  (D)

Hit Kudos if this helped!

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pankajpatwari · Answer

What is the logic behind providing additional info of '5 points distance'?? The question can be solved without that..just calculate the equation of line by point slope form formula and put the options in the equation..the ones which satisfy the equation are correct... Right??

stne · Answer

There are two conditions point B should meet :
1) It should satisfy the Eqn: y= (-3/4)x + 9
2) Point B should be 5 units from (4 6)

Lets say there was another point (12, 0) in the option you will see that this also meets the eqn. of the line. But the distance of this point from (4 6) is 10 and NOT 5.

Lets say the answer choices were:
I. (8, 3) 
II. (1, 10) 
III. (0, 9)
IV.( 12 0)
V( 16 -3)

You would see that only I and III meet both the conditions and is the correct answer, options IV and V meet condition 1 but NOT condition 2. Hence it is important to mention the second condition.

Hope this answer your query.

Hi  LeoN88 , 
Thank you for your soln. but there is a small typo in the second last line and the line before that. You have I and II instead of I and III. Hope you will look into it. Thanks.

LeoN88 · Answer

edited, thanks.

bumpbot · Answer

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Point A(4, 6) lies on a line with slope -3/4 Point B lies on the same

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Point A(4, 6) lies on a line with slope -3/4 Point B lies on the same

Prep Toolkit

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