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Question: If the points \((a,b),(a',b')\) and \((a - a',b - b')\) are collinear, then....

If the points (a,b),(a′,b′)(a,b),(a',b') and (a−a′,b−b′)(a - a',b - b') are collinear, then.

A

ab′=a′bab' = a'b

B

ab=a′b′ab = a'b'

C

aa′=bb′aa' = bb'

D

a2+b2=1a^{2} + b^{2} = 1

Answer

ab′=a′bab' = a'b

Explanation

Solution

a−a′−a′a′−a=b−b′−b′b′−b\frac { a - a ^ { \prime } - a ^ { \prime } } { a ^ { \prime } - a } = \frac { b - b ^ { \prime } - b ^ { \prime } } { b ^ { \prime } - b }

⇒a−2a′a′−a=b−2b′b′−b\Rightarrow \frac { a - 2 a ^ { \prime } } { a ^ { \prime } - a } = \frac { b - 2 b ^ { \prime } } { b ^ { \prime } - b } ⇒aa′=bb′⇒ab′=a′b\Rightarrow \frac { a } { a ^ { \prime } } = \frac { b } { b ^ { \prime } } \Rightarrow a b ^ { \prime } = a ^ { \prime } b