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Straight Lines

Theory and Formula


Question

Q1. Which statement is true:

(a) Centroid of a triange is the point of concurrence of median.

(b) Centroid, generally denoted by G.

(c) Centroid divides each median in the ratio 2:1 internally.

(d) all the above.

Solution.
(d) All the above
Solution

Q2. Find the equation of the line whose slope is 2 and which cuts-off 6 units along y-axis.

Let the equation of line is y = mx + c (single slope form of a line), where m = slope and c = intercept part.

y = 2x + 6
Solution

Q3. : (a) Three points are collinear, if area of triangle developed by these three points is zero Which statement is true

(a) Three points are collinear, if area of triangle developed by these three points is zero.

(b) Two line are parallel if m1 = m2.

(c) Two lines are perpendicular if m1.m2 = -1

(d) All the above.

Solution.
(d) All the above
Solution

Q4. Line 8x + 15y = 120 cuts x and y axis at A and B respectively. Find the distance between A and B .

(a) 17 (b) 8 (c) 15 (d) 20

Solution.


AB2 = OB2 + AO2

AB2 = 64 + 225

AB = 17
Solution

Q5. Find the equation of line which has equal intercept and passes through the point (2,3).

(a) x+y = 2 (b) x = y (c) x + y = 5 (d) x + y = 7

Solution.
x/a + 4/b = 1

∴ a = b

x/a + y/a = 1

(x + y)/a = 1

x + y = a

2 + 3 = a

a = 5

x + y = 5
Solution

Q6. One side of rectangle lies along the line 4x - 7y + 3 = 0, Two of its vertices are (1,1) and (-2,1),find the equationof side which is parallel to given line.

(a) 4x + 7y + 15 = 0 (b) 4x - 7y + 15 = 0 (c) 4x - 9y + 3 = 0 (d) 4x - 7y - 15 = 0

Solution.
(b) 4x - 7y + 15 = 0

Point (1,1) lies on the given line. so point (-2,1) lies on the another line which is parallel to given line .

4x - 7y + k = 0

4(-2) - 7(1) + k = 0

-8 - 7 + k = 0

-15 + k = 0

k = 15
Solution

Q7. Line y = 3x will passes through origin
(a) True (b) False (c) Can't say (d) None of these

Solution.
True
Note : y = 3x has no pure constant , that is why this line passes through the origin
Solution

Q8. The slope of the tangent to the curve y = √(4 - x2) at the point where the ordinate and the abscissa are equal is

(a) 0 (b) 1 (c) 2 (d) -1

Solution.
(d) -1
Solution

Q9. Find the equation of a line parallel to the line joining the points (5,3) and (2,9) , which passes through the points .(3,-4)

(a) y + 2x - 2 = 0 (b) y + 2x = 0 (c) y - 4x + 6 = 0 (d) y - 2x - 2 = 0

Solution.
(a) y + 2x - 2 = 0
Solution

Q10. The four lines ax ± by ± c = 0 , enclose a rhombus whose area is .

(a) 2a2/abc (b) abc (c) 2/ab (d) 2c2/ab

Solution.
(d) 2c2/ab
Solution