Coordinate Geometry - Study Mode

[#56] If ax - 4y = -6 has a slope of $$ - frac{3}{2}.$$ xa0What is the value of a?
Correct Answer

(C) -6

Explanation

Solution: $$eqalign{
& ax - 4y = - 6 cr
& Rightarrow 4y = ax + 6 cr} $$ $$eqalign{
& y = frac{a}{4}x + frac{6}{4} cr
& frac{a}{4} = frac{{ - 3}}{2} cr
& x08oxed{a = - 6} cr} $$

[#57] What is the area (in sq. units) of the triangle formed by the graphs of the equations 2x + 5y - 12 = 0, x + y = 3 and y = 0?
Correct Answer

(A) 3

Explanation

Solution: 2x + 5y - 12 = 0 x + y = 3 at y = 0 (3, 0), (6, 0) at x = 0 (0, 2.4)(0, 3) Area of Δ = $$frac{1}{2}$$ × 3 × 2 = 3

[#58] What is the slope of the line perpendicular to the line passing through the points (-5, 1) and (-2, 0)?
Correct Answer

(B) 3

Explanation

Solution: Slope of the line passing through the point (-5, 1) & (-2, 0) $${m_1} = frac{{0 - 1}}{{ - 2 - left( { - 5}
ight)}} = frac{{ - 1}}{3},,,,,left[ {m = frac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}}}
ight]$$ Slope of the 1 st line $$ = frac{{ - 1}}{{{m_1}}} = frac{{ - 1}}{{left( {frac{{ - 1}}{3}}
ight)}} = 3$$ (∴ If 2 lines are ⊥ then their slope m 1 × m 2 = -1)

[#59] For what value of m will the system of equations 18x - 72y + 13 = 0 and 7x - my - 17 = 0 have no solution?
Correct Answer

(A) 28

Explanation

Solution: 18x - 72y + 13 = 0 7x - my - 17 = 0 There is no solution, means they are parallel $$eqalign{
& frac{{{a_1}}}{{{a_2}}} = frac{{{b_1}}}{{{b_2}}} cr
& Rightarrow frac{{18}}{7} = frac{{72}}{m} cr
& Rightarrow m = 7 imes 4 cr
& Rightarrow m = 28 cr} $$

[#60] The points A(3, -2), B(1, 4) and C(-2, x) are collinear. What is the value of x?
Correct Answer

(A) 13

Explanation

Solution: A(3, -2), B(1, 4), C(-2, x) Condition for collinearity of three points 0 = x 1 (y 2 - y 3 ) + x 2 (y 3 - y 1 ) + x 3 (y 1 - y 2 ) 0 = 3(4 - x) + 1(x + 2) + (-2)(-2 - 4) 0 = 12 - 3x + x + 2 + 12 2x = 26 x = 13 Alternate Solution: For collinear condition slope will be same $$eqalign{
& frac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}} = frac{{{y_3} - {y_2}}}{{{x_3} - {x_2}}} cr
& frac{{4 + 2}}{{1 - 3}} = frac{{x - 4}}{{ - 2 - 1}} cr
& frac{6}{{ - 2}} = frac{{x - 4}}{{ - 3}} cr
& 9 = x - 4 cr
& x = 13 cr} $$