CBSE Class 11 Mathematics Straight Lines Worksheet Set A

Multiple Choice Questions

Question. The point (− 3, 2) is located in the quadrant
(a) quadrant I
(b) quadrant II
(c) quadrant III
(d) quadrant IV
Answer : B

Question. A triangle ABC lying in the first quadrant has two vertices as A (1, 2) and B(3, 1). If ∠BAC = 90°, and ar (ΔABC) = 5√5 sq. units, then the abscissa of the vertex C is:
(a) 1+ √5
(b) 1+ 2√5
(c) 2 + √5
(d) 2√5 -1
Answer : B

Question. A triangle has a vertex at (1, 2) and the mid points of the two sides through it are (–1, 1) and (2, 3). Then the centroid of this triangle is :
(a) (1, 7/3)
(b) (1/3, 2)
(c) (1/3, 1)
(d) (1/3, 5/3)
Answer : B

Question. Let the orthocentre and centroid of a triangle be A(–3, 5) and B(3, 3) respectively. If C is the circumcentre of this triangle, then the radius of the circle having line segment AC as diameter, is :
(a) 2√10
(b) 3√5/2
(c) 3√5/2
(d) 10
Answer : B

Question. A light ray emerging from the point source placed at P( l, 3) is reflected at a point Q in the axis of x. If the reflected ray passes through the point R (6, 7), then the abscissa of Q is:
(a) 1
(b) 3
(c) 7/2
(d) 5/2
Answer : D

Question. Let A (h, k), B(1, 1) and C (2, 1) be the vertices of a right angled triangle with AC as its hypotenuse. If the area of the triangle is 1square unit, then the set of values which 'k' can take is given by
(a) {–1, 3}
(b){–3, –2}
(c) {1, 3}
(d) {0, 2}
Answer : A

Question. A square, of each side 2, lies above the x-axis and has one sertex at the origin. If one of the sides passing through the origin makes an angle 30 with the positive direction of the x-axis, then the sum of the x-coordinates of the vertices of the square is :
(a) 2√3 -1
(b) 2√3 - 2
(c) √3 - 2
(d) √3 -1
Answer : B

Question. If a straight line passing through the point P(–3, 4) is such that its intercepted portion between the coordinate axes is bisected at P, then its equation is :
(a) 3x – 4y + 25 = 0
(b) 4x – 3y + 24 = 0
(c) x – y + 7 = 0
(d) 4x + 3y = 0
Answer : B

Question. Let L be the line passing through the point P(1, 2) such that its intercepted segment between the co-ordinate axes is bisected at P. If L1 is the line perpendicular to L and passing through the point (–2, 1), then the point of intersection of L and L1 is :
(a) (4/5, 12/5)
(b) (3/5, 23/10)
(c) (11/20, 29/10)
(d) (3/10, 17/5)
Answer : A

Question. Two vertices of a triangle are (0, 2) and (4, 3). If its orthocentre is at the origin, then its third vertex lies in which quadrant?
(a) third
(b) second
(c) first
(d) fourth
Answer : B

Question. If the perpendicular bisector of the line segment oining the points P (1, 4) and Q (k, 3) has y-intercept equal to – 4, then a value of k is :
(a) – 2
(b) – 4
(c) √14
(d) √15
Answer : B

Question. The points (0, 8/3) (1, 3) and (82, 30) :
(a) form an acute angled triangle.
(b) form a right angled triangle.
(c) lie on a straight line.
(d) form an obtuse angled triangle.
Answer : C

Question. Locus of centroid of the triangle whose vertices are (a cos t, asin t), (bsin t,- bcos t) and (1, 0), where t is a parameter, is
(a) (3x +1)² + (3y)² = a² - b²
(b) (3x -1)² + (3y)² = a² - b²
(c) (3x -1)² + (3y)² = a² + b²
(d) (3x +1)² + (3y)² = a² + b²
Answer : C

Question. If a ΔABC has vertices A(–1, 7), B(–7, 1) and C(5, –5), then its orthocentre has coordinates :
(a) (- 3/5, 3/5)
(b) (-3, 3)
(c) (3/5, - 3/5)
(d) (3, -3)
Answer : B

Question. A ray of light is incident along a line which meets another line, 7x – y + 1 = 0, at the point (0, 1). The ray is then reflected from this point along the line, y + 2x = 1. Then the equation of the line of incidence of the ray of light is :
(a) 41x – 25y + 25 = 0
(b) 41x + 25y – 25 = 0
(c) 41x – 38y + 38 = 0
(d) 41x + 38y – 38 = 0
Answer : C

Question. A triangle with vertices (4, 0), (–1, –1), (3, 5) is
(a) isosceles and right angled
(b) isosceles but not right angled
(c) right angled but not isosceles
(d) neither right angled nor isosceles
Answer : A

Question. Let C be the centroid of the triangle with vertices (3, –1), (1, 3) and (2, 4). Let P be the point of intersection of the lines x + 3y – 1 = 0 and 3x – y + 1 = 0. Then the line passing through the points C and P also passes through the point:
(a) (–9, –6)
(b) (9, 7)
(c) (7, 6)
(d) (–9, –7)
Answer : A

Question. Let O(0, 0) and A(0, 1) be two fixed points. Then the locus of a point P such that the perimeter of ΔAOP is 4, is :
(a) 8x² – 9y² + 9y = 18
(b) 9x² – 8y² + 8y = 16
(c) 9x² + 8y² – 8y = 16
(d) 8x² + 9y² – 9y = 18
Answer : C

Question. The slope of line, whose inclination is 60°, is
(a) 1/√3
(b) 1
(c) 3
(d) Not defined
Answer : C

Question. Area of the triangle whose vertices are (4, 4), (3, −2) and (− 3, 16), is
(a) 54
(b) 27
(c) 53
(d) 106
Answer : B

Question. The value of y is, if the distance between points P (2, − 3) andQ (10, y ) is 10 units.
(a) 3
(b) 9
(c) − 3
(d) None of these
Answer : A

Question. The line passing through the points (− 4, 5) and (− 5, 7) also passes through the point (l , m), then 2l + m + 3 is equal to
(a) 1
(b) −1
(c) 2
(d) 0
Answer : D

Question. The angle between the lines y = (2 − √3)(x +5) and y = (2 + √3)(x − 7) is
(a) 30°
(b) 90°
(c) 45°
(d) 120°
Answer : D

Question. The angle between the X -axis and the line joining the points (3, − 1) and (4, − 2) is
(a) 45°
(b) 135°
(c) 90°
(d) 180°
Answer : B

Question. If the vertices of a triangle are P (1, 3), Q (2, 5) and R(3, − 5), then the centroid of a DPQR is
(a) (1, 2)
(b) (1, 3)
(c) (3, 1)
(d) (2, 1)
Answer : D

Question. The value of y will be, so that the line through (3, y ) and (2, 7) is parallel to the line through (−1, 4) and (0, 6).
(a) 7
(b) 8
(c) 9
(d) 10
Answer : B

Question. A line cutting off intercept −3 from the Y-axis and the tangent at angle to the X-axis is 3/5, its equation is
(a) 5y − 3x + 15 = 0
(b) 3y −5x + 15 = 0
(c) 5y − 3x −15 = 0
(d) None of these
Answer : A

Question. The points A (x, 4), B (3, − 2) and C (4, − 5) are collinear in the value of x is
(a) 1
(b) 2
(c) −1
(d) 0
Answer : A

Question. The point on X-axis which is equidistant from the points (3, 2) and (−5, − 2) is
(a) (1, 0)
(b) (2, 0)
(c) (−1,0)
(d) (−2,0)
Answer : C

Question. The slope of a line whose inclination is 90°, is
(a) 1
(b) 0
(c) −1
(d) not defined
Answer : D

Question. The equation of the lines parallel to the X-axis and passing through the point (− 3, 5) is
(a) x = − 3
(b) y = − 3
(c) x = 5
(d) y = 5
Answer : D

Assertion-Reasoning MCQs

Directions Each of these questions contains two statements : Assertion (A) and Reason (R). Each of these questions also has four alternative choices, any one of which is the correct answer. You have to select one of the codes (a), (b), (c) and (d) given below.
(a) A is true, R is true; R is a correct explanation for A.
(b) A is true, R is true; R is not a correct explanation for A.
(c) A is true; R is false.
(d) A is false; R is true.

Question. Assertion (A) Area of the triangle whose vertices are (4, 4), (3, −2) and (− 3, 16), is
Reason (R) Area of triangle whose vertices are (x₁, y₁), (x₂ , y₂ ) and (x₃ , y₃ ), is 1/2 | x₁ (y₂ − y₃) + x₂ (y₃ − y₁) + x₃ (y₁ − y₂ ) |.
Answer : A

Question. Assertion (A) If x cosq + y sin q = 2 is perpendicular to the line x − y = 3, then one of the value of θ is π/4.
Reason (R) If two lines y = m₁ x + c₁ and y = m₂ x + c₂ are perpendicular then m₁ = m₂.
Answer : C

Question. Assertion (A) The point (3, 0) is at 3 units distance from theY -axis measured along the positive X -axis and has zero distance from the X -axis.
Reason (R) The point (3, 0) is at 3 units distance from the X -axis measured along the positiveY -axis and has zero distance from theY -axis.
Answer : C

Question. If the vertices of a triangle are (1, a), (2, b ) and (c² , − 3 ). Then,
Assertion (A) The centroid cannot lie on the Y-axis.
Reason (R) The condition that the centroid may lie on the X-axis is a + b = 3.
Answer : B

Question. Assertion (A) The slope of the line x + 7y = 0 is 1/7 and y-intercept is 0.
Reason (R) The slope of the line 6x + 3y − 5 = 0 is − 2 and y-intercept is 5/3
Answer : B

Question. Assertion (A) Slope of X -axis is zero and slope ofY -axis is not defined.
Reason (R) Slope of X -axis is not defined and slope ofY -axis is zero.
Answer : C

Question. Assertion (A) Slope of line 3x − 4y + 10 = 0 is 3/4.
Reason (R) x-intercept and y-intercept of 3x − 4y + 10 = 0 respectively are − 10/3 and 5/2
Answer : B

Question. If the equation of line is x − y = 4, then
Assertion (A) The normal form of same equation is x cosa + y sin a = p, where a = 315° and p = 2√2.
Reason (R) The perpendicular distance of line from the origin is 3√2.
Answer : C

Question. If A (− 2, − 1), B (4, 0),C (3, 3) and D (− 3, 2) are the vertices of a parallelogram, then 
Assertion (A) Slope of AB = Slope of BC and Slope ofCD = Slope of AD.
Reason (R) Mid-point of AC = Mid-point of BD
Answer : D

Case Based MCQs

Four friends Rishabh, Shubham, Vikram and Rajkumar are sitting on vertices of a rectangle, whose coordinates are given.

Based on the above information answer the following questions.

Question. The equation formed by Shubham and Rajkumar is
(a) x + 2y + 3 =0
(b) x −2y − 3 =0
(c) x −2y + 3 =0
(d) None of the above
Answer : C

Question. The equation formed by Rishabh and Vikram is
(a) x + 2y + 9 =0
(b) x + 2y −9 =0
(c) x −2y −9 =0
(d) None of the above
Answer : B

Question. The intersection point of above two equations is
(a) (1, 1)
(b) (2, 2)
(c) (3, 3)
(d) (4, 4)
Answer : C

Question. Slope of equation of line formed by Rishabh and Rajkumar is
(a) zero
(b) 1
(c) 2
(d) 3
Answer : A

Question. Pair for the same slope is
(a) Rishabh-Rajkumar and Shubham-Vikram
(b) Rishabh-Rajkumar and Rajkumar-Vikram
(c) Rishabh-Rajkumar andRishabh-Shubham
(d) None of the above
Answer : A

Click on link below to download CBSE Class 11 Mathematics Straight Lines Worksheet (2).