Coordinate Geometry Question 153
Question: If the points $ A(3,4),B(7,7),C(a,b) $ be collinear and $ AC=10 $ , then $ (a,b) $ =
Options:
A) $ (11,10) $
B) $ (10,11) $
C) $ (11/2,5) $
D) $ (5,11/2) $
Show Answer
Answer:
Correct Answer: A
Solution:
$ {{(a-3)}^{2}}+{{(b-4)}^{2}}=100 $ and $ \frac{b-7}{3}=\frac{a-7}{4} $
Hence (a, b)=(11, 10).
Trick: Check with options. We find that the point (11, 10) satisfies both the conditions i.e. $ AC=\sqrt{{{(11-3)}^{2}}+{{(10-4)}^{2}}}=10 $ . Also this is collinear with A, B.
BETA
