Coordinate Geometry Question 76
Question: The points of trisection of the line segment joining the points (3, -2) and (-3, -4) are
Options:
A) $ ( \frac{3}{2},-\frac{5}{2} ),( -\frac{3}{2},-\frac{13}{4} ) $
B) $ ( -\frac{3}{2},\frac{5}{2} ),( \frac{3}{2},\frac{13}{4} ) $
C) $ ( 1,-\frac{8}{3} ),( -1,-\frac{10}{3} ) $
D) None of these
Show Answer
Answer:
Correct Answer: C
Solution:
Let $ A(3,-2) $ , $ B(-3,-4) $ and two points C and D are the trisection points of AB. Obviously C divides the line AB in 1 : 2, therefore coordinates of C are $ ( \frac{1(-3)+2(3)}{1+2},\frac{1(-4)+2(-2)}{1+2} )=( 1,-\frac{8}{3} ) $ . Similarly D divides the line AB in 2 : 1, hence coordinates of D are $ ( \frac{2(-3)+1(3)}{2+1},\frac{2(-4)+1(-2)}{2+1} )=( -1,-\frac{10}{3} ) $ .
BETA
