Question

Find the coordinate of a point which divides the join of (-1,7) and (4,-3) in the ratio 2:3

Answer 1

(x1,y1) is (-1,7)
(x2,y2) is (4,-3)
m1=2
m2=3

x = m1x2+m2x1/m1+m2
= (2×4)+(3×-1)/(2+3) = (8-3)/5
= 5/5 = 1

y = m1y2+m2y1/m1+m2
= (2×-3)+(3×7)/(2+3) = (-6+21)/5
= 15/5 = 3

So, the point is (1,3)

Answer 2

Given : A point which divides the join of (-1,7) and (4,-3) in the ratio 2:3

To find : The coordinates of that point.

Solution :

We can simply solve this mathematical problem by using the following mathematical process. (our goal is to calculate the coordinates of the said point)

If the two coordinates of two endpoints of a straight line are, (x1,y1) and (x2,y2). And, the straight line is (internally) divided into m:n ratio, then the coordinates of the point which divides that straight line will be :

$= ( \frac{mx2 +nx1 }{m + n} ),( \frac{my2 + ny1}{m + n} )$

In this case,

m : n = 2 : 3

or,

m = 2 , and , n = 3

And,

(x1,y1) = (-1,7)

(x2,y2) = (4,-3)

So, the coordinates of the point will be :

$= ( \frac{(2 \times 4) + (3 \times ( - 1))}{2 + 3} ),( \frac{(2 \times( - 3)) + (3 \times 7) }{2 + 3} )$

= (1,3)

(This will be considered as the final result of the given mathematical problem.)

Hence, the coordinates of the point are (1,3)