Question

X(2,3) and Z(4,6) are two given points and the point y divides the line segment XZ externally in the ratio 3:4. Find the coordinate of y

Answer 1

Answer:

answer is

$( \frac{20}{7} . \frac{30}{7} )$

Answer 2

ANSWER :-

(-4,-6)

PROCEDURE :-

Since given the points X(2,3) Z(4,6) are divided by a point y in the ratio 3:4 externally ,

FORMULA USED :-

When two line joining points A (a,b) and B(c,d) are divided in the ratio l:m EXTERNALLY by a point p(x,y), then coordinates of p are obtained by

$p(x,y) = ( \frac{lc - ma}{l - m} , \frac{ld - mb}{l - m} )$

NOTE :-

Don't get confused with the formula that we use to get the ratio when point divides internally.

SOLUTION :-

COMPARING THE TERMS INTRODUCED BY ME AND THE TERMS GIVEN IN THE QUESTION , HERE ,

• A = X
• B = Y
• p = y
• a = 2
• b = 3
• c = 4
• d = 6
• l = 3
• m = 4

NOW SUBSTITUTING THE GIVEN VALUES IN THE FORMULA , WE GET ,

$p(x,y) = ( \frac{lc - ma}{l - m} , \frac{ld - mb}{l - m} ) \\ \\p(x,y) = ( \frac{3(4) - 4(2)}{3 - 4} , \frac{3(6) - 4(3)}{3- 4} ) \\ \\ p(x,y) = ( \frac{12 - 8}{ - 1} , \frac{18 - 12}{ - 1} ) \\ \\ p(x,y) = ( - 4, - 6)$

THERE FORE ACCORDING TO THE QUESTION , THE COORDINATES OF y are (-4,-6)