Coordinate Geometry Question 58
Question: The coordinates of the points A, B, C are $ (x_1,y_1) $ , $ (x_2,y_2) $ , $ (x_3,y_3) $ and D divides the line AB in the ratio l : k. If P divides the line DC in the ratio m : k + l, then the coordinates of P are
Options:
A) $ ( \frac{kx_1+lx_2+mx_3}{k+l+m},\frac{ky_1+ly_2+my_3}{k+l+m} ) $
B) $ ( \frac{lx_1+mx_2+kx_3}{l+m+k},\frac{ly_1+my_2+ky_3}{l+m+k} ) $
C) $ ( \frac{mx_1+kx_2+lx_3}{m+k+l},\frac{my_1+ky_2+ly_3}{m+k+l} ) $
D) None of these
Show Answer
Answer:
Correct Answer: A
Solution:
Coordinates of D will be $ ( \frac{lx_2+kx_1}{l+k},\frac{ly_2+ky_1}{l+k} ) $ Now again, DC is divided by P in $ m:k+l. $ Then the coordinates of P will be given by $ ( \frac{mx_3+lx_2+kx_1}{k+l+m},\frac{my_3+ly_2+ky_1}{k+l+m} ) $ .
BETA
