Question

Statement -1 : The line 3x + 2y = 24 meets the coordinates axes at A and B , and the perpendicular bisector of AB meets the line through (0,-1) parallel to the x-axis at C . The area of `Delta` ABC is 91 square units .
Statement-2 : Area of the triangle with vertices at (a,0) , (0,b) and (a , b) is ab/2 sq. units .
A. Statement -1 is True , Statement - 2 is true , Statement- 2 is a correct explanation for statement - 8
B. Statement-1 is True , Statement-2 is True , Statement -2 is not a correct explanation for Statement - 1 .
C. Statement-1 is True , Statement - 2 is False .
D. Statement - 1 is False , Statement -2 is True .

Answer 1

Correct Answer - B
The line 3x + 2y = 24 meets the coordinate axes at A (8,0) , B( 0 , 12) . The coordinates of the mid-point D of AB are (4,6) . Equation of the perpendicular bisector of AB is 2x - 3y + 10 = 0
This meets the line through (0 ,-1) parallel to the x-axis i.e.
y = -1 at C (-13/2 , -1) .
`therefore` Area of `DeltaABC = (1)/(2) AB xx CD`
`implies` Area of `Delta ABC = (1)/(2) sqrt(64 + 144) xx sqrt(((13)/(2) + 4)^(2) + (1-6)^(2))`
`implies` Area of `Delta ABC = (1)/(2) xx sqrt(208) xx 7 sqrt((9)/(4) + 1) = 91` sq. units
So , statement-1 is true .
The area of the triangle with vertices at (a,0) , (0, b) and (a , b) is
Absolute value of `(1)/(2) |{:(a , b , 1), (0 , b , 1) , (a , b , 1):}| = (1)/(2)` ab sq. units .
So , statement - 2 is true . But , statement - 2 is not a correct explanation for statement - 1 .