Q: What are the coordinates for the point on line A(-5,6) and (-2,0) that is 3 times as far from b, and that is in between points A and B?
could you please help me break down in a more understandable process to solve this problem in a short time period. Thank you in advance!
Coordinate plane problem
This topic has expert replies
- iwillsurvive101
- Senior | Next Rank: 100 Posts
- Posts: 58
- Joined: Mon Nov 07, 2011 7:44 pm
- Location: Washington DC
- Thanked: 1 times
I've seen these types of questions in OG. I try to solve them by logic, trying each point in the answer choice and make sure it satisfies the "how far" requirement.
An algebraic approach would be better.
An algebraic approach would be better.
- aneesh.kg
- Master | Next Rank: 500 Posts
- Posts: 385
- Joined: Mon Apr 16, 2012 8:40 am
- Location: Pune, India
- Thanked: 186 times
- Followed by:29 members
If a Point P(x,y) divides Point A(x1, y1) and B(x2, y2) in the ratio of a:b, then the co-ordinates of point P are:
x = (a*x2 + b*x1) / (a + b)
y = (a*y2 + b*y1) / (a + b)
(Notice that it's a cross ratio)
In the problem stated by you, if A(x1, y1) = (-5, 6) and B(x2, y2) = (2, 0) and the required Point P(x,y) divides A and B in a:b = 3:1
Use the formula above, and get the answer.
x = (a*x2 + b*x1) / (a + b)
y = (a*y2 + b*y1) / (a + b)
(Notice that it's a cross ratio)
In the problem stated by you, if A(x1, y1) = (-5, 6) and B(x2, y2) = (2, 0) and the required Point P(x,y) divides A and B in a:b = 3:1
Use the formula above, and get the answer.
Aneesh Bangia
GMAT Math Coach
[email protected]
GMATPad:
Facebook Page: https://www.facebook.com/GMATPad
GMAT Math Coach
[email protected]
GMATPad:
Facebook Page: https://www.facebook.com/GMATPad
- Shalabh's Quants
- Master | Next Rank: 500 Posts
- Posts: 134
- Joined: Fri Apr 06, 2012 3:11 am
- Thanked: 35 times
- Followed by:5 members
I have rewritten the question stem. There is something missing in it.rajman41 wrote:Q: What are the coordinates for the point on line A(-5,6) and (-2,0) that is 3 times as far from b, and that is in between points A and B?
could you please help me break down in a more understandable process to solve this problem in a short time period. Thank you in advance!
What are the co-ordinates for the point on line A(-5,6) and B(-2,0) that is 3 times as far from B as from A, and that is in between points A and B?
Say The point 3 times farther from B is C. So A, C & B are co-linear & lying on the line in that orer. We can say AC:BC::1:3
Say the co-ordinates of C is (x,y).
Co-ordinates of a point that intersects a line in the ratio of m:n is given by
x = (mx1+nx2)/(m+n) & y = (my1+ny2)/(m+n); here (x1,y1)=(-5,6) i.e. point A & (x2,y2)=(-2,0) i.e. point B.
x = (3.-5+1.-2)/(3+1) = -32/4 = -8 & y = (3.6+1.0)/(3+1) = 18/4 = 9/2. So the point is (-8,9/2).
Shalabh Jain,
e-GMAT Instructor
e-GMAT Instructor