among the lines passing through C(3, 1). BA is farthest from the origin and cuts the x-axis and y-axis at A and B respectively then the ratio of BC to CA is?
Answers
BC : CA = 9 : 1
Step-by-step explanation:
BA is the farthest line from the origin then it must be perpendicular to the line joining origin and the point (3,1)
Line joining (0,0) & ( 3 , 1)
slope = 1 /3
y = x/3
Slope of perpendicular line
- 3
y = - 3x + c
passing through (3 , 1)
=>1 = - 3 *3 + c
=> c = 10
=>y = - 3x + 10
Cut x axis at A
0 = -3A + 10
=> A = 10/3
A = (10/3 , 0)
Cut y axis at B
=> B = 10
=> B = (0 , 10)
BC (0, 10) & ( 3 , 1)
= √(3 - 0)² + (1 - 10)²
= √9 + 81
= √90
= 3√10
CA ( 3 , 1) (10/3 , 0)
CA = √(10/3 - 3)² + (0 - 1)²
= √1/9 + 1
= √10/9
= √10 / 3
BC : CA = 3√10 : √10 / 3
=> BC : CA = 9 : 1
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