Coordinate Geometry - Study Mode

[#26] What is the equation of the line which intercepts x-axis and y-axis at $$frac{3}{4}$$ and $$ - frac{2}{3}$$ respectively?
Correct Answer

(C) 8x - 9y = 6

Explanation

Solution: Equation of line which intercepts x-axis and y-axis are given below:- $$eqalign{
& Rightarrow frac{x}{a} + frac{y}{b} = 1 cr
& { ext{where, }}a = frac{3}{4},,b = frac{{ - 2}}{3},,left[ {{ ext{given}}}
ight] cr
& Rightarrow frac{x}{{frac{3}{4}}} + frac{y}{{frac{{ - 2}}{3}}} = 1 cr
& Rightarrow frac{{4x}}{3} - frac{{3y}}{2} = 1 cr
& Rightarrow 8x - 9y = 6 cr} $$

[#27] The graphs of the equations 3x + y - 5 = 0 and 2x - y - 5 = 0 intersect at the point P(α, β). What is the value of (3α + β)?
Correct Answer

(B) 5

Explanation

Solution: $$eqalign{
& 3x + y = 5 cr
& underline {2x - y = 5} cr
& 5x = 10 cr
& x = 2,,y = - 1 cr
& left( {alpha ,,x08eta }
ight) = left( {2,, - 1}
ight) cr
& 3alpha + x08eta = 3 imes 2 - 1 = 5 cr} $$

[#28] The line passing through point (-3, 1) and point (x, 5) is parallel to the line passing through point (-2, -1) and point (6, 3). What is the value of x?
Correct Answer

(D) 5

Explanation

Solution: Slope (m 1 ) for the line which passes through the points (-3, 1) and (x, 5) $$ = frac{{5 - 1}}{{x + 3}} = frac{4}{{x + 3}}$$ Similarly, slope (m 2 ) for the line which passes through the points (-2, -1) and (6, 3) $$ = frac{{3 + 1}}{{6 + 2}} = frac{4}{8} = frac{1}{2}$$ If two lines are parallel to each other. $$eqalign{
& { ext{Then, }}{m_1} = {m_2} cr
& Rightarrow frac{4}{{x + 3}} = frac{1}{2} cr
& Rightarrow x + 3 = 8 cr
& Rightarrow x = 5 cr} $$

[#29] Slope of the line AB is $$ - frac{2}{3}.$$ xa0Co-ordinates of points A and B are (x, -3) and (5, 2) respectively. What is the value of x?
Correct Answer

(C) 12.5

Explanation

Solution: Given, $$eqalign{
& m = frac{{ - 2}}{3} cr
& m = frac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}} cr
& Rightarrow frac{{ - 2}}{3} = frac{{2 + 3}}{{5 - x}} cr
& Rightarrow frac{{ - 2}}{3} = frac{5}{{5 - x}} cr
& Rightarrow - 10 + 2x = 15 cr
& Rightarrow 2x = 25 cr
& Rightarrow x = 12.5 cr} $$

[#30] The equation of a straight line on a point (3, -5) and slope 2 is:
Correct Answer

(A) 2x - y - 11 = 0

Explanation

Solution: Point (a, b) = (3, -5) Slope = 2 The general equation of a straight line (y - b) = m(x - a) (y + 5) = 2(x - 3) y + 5 = 2x - 6 2x - y - 11 = 0