Coordinate Geometry - Study Mode

[#51] In what ratio is the segment joining points (2, 3) and (-2, 1) divided by the Y-axis?
Correct Answer

(B) 1 : 1

Explanation

Solution: $$eqalign{
& frac{{k:1}}{{{ ext{A}}left( { - 2,,1}
ight),,,,,,,,,,{ ext{C}}left( {x,,y}
ight),,,,,,,,,,{ ext{B}}left( {2,,3}
ight)}} cr
& Rightarrow x = frac{{ - 2k + 2}}{{k + 1}} cr
& { ext{At }}y{ ext{ - axis}},x08oxed{x = 0} cr
& herefore 0 = frac{{ - 2k + 2}}{{k + 1}} cr
& Rightarrow x08oxed{k = 1} cr
& { ext{Ratio}} = 1:1 cr} $$

[#52] The equations 3x + 4y = 10 and -x + 2y = 0, have the solution (a, b). The value of a + b is:
Correct Answer

(C) 3

Explanation

Solution: 3x + 4y = 10 . . . . . . . (i) -x + 2y = 0 . . . . . . . (ii) On solving both the equation 3(2y) + 4y = 10 10y = 10 y = 1 ∴ x = 2 × 1 = 2 ∴ Solution (a, b) = (2, 1) ∴ a + b = 2 + 1 = 3

[#53] Find equation of the perpendicular to segment joining the points A(0, 4) and B(-5, 9) and passing through the point P. Point P divides segment AB in the ratio 2 : 3.
Correct Answer

(B) x - y = -8

[#54] What is the equation of the line passing through the point (-1, 3) and having x-intercept of 4 units?
Correct Answer

(B) 3x + 5y = 12

Explanation

Solution: Slope (m 1 ) for the line PQ $$ = frac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}} = frac{{0 - 3}}{{4 + 1}} = frac{{ - 3}}{5}$$ Now, required equation of the line passing through (-1, 3) and having x-intercept of 4 $$eqalign{
& y = mleft( {x - a}
ight) cr
& Rightarrow y = - frac{3}{5}left( {x - 4}
ight) cr
& Rightarrow 5y = - 3x + 12 cr
& Rightarrow 3x + 5y = 12 cr} $$

[#55] ABCD is a parallelogram. Co-ordinates of A, B and C are (5, 0), (-2, 3) and (-1, 4) respectively. What will be the equation of line AD?
Correct Answer

(D) y = x - 5

Explanation

Solution: Parallelogram ABCD AD || BC Slope of line AD (m) = Slope of line BC Slope of line BC $$ = frac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}} = frac{{4 - 3}}{{ - 1 + 2}} = 1$$ Slope of AD = 1 Equation of line AD ⇒ y - y 1 = m(x - x 1 ) x 1 = 5, y 1 = 0 y - 0 = 1(x - 5) y = x - 5