CBSE Class 10 Mathematics Coordinate Geometry MCQs Set 09

Question. PQOR is a rectangle whose vertices are Q (0, 7), O (0, 0) and R (- 5, 0). Find the length of its diagonal.
(a) \(\sqrt{84}\)
(b) 8
(c) 12
(d) \(\sqrt{74}\)
Answer: D

Question. The point which lies on the perpendicular bisector of the line segment joining the points P (- 3, - 5) and Q (3, 5) is
(a) (-3, 4)
(b) (2, -5)
(c) (0, 0)
(d) (-1, 4)
Answer: C

Question. The points (- 5, 0), (0, 4) and (5, 1) are the vertices of a _______
(a) right triangle
(b) isosceles triangle
(c) equilateral triangle
(d) scalene triangle
Answer: D

Question. The points (4, 5), (6, 7) and (8, 9) are ________
(a) collinear
(b) not collinear
(c) the vertices of a right triangle
(d) vertices of an isosceles triangle
Answer: A

Question. If a point (x, y) is equidistant from the points (p + q, q - p) and (p - q, p + q), then ________
(a) \(qx + yp = 0\)
(b) \(qx = yp\)
(c) \(px = qy\)
(d) \(px + qy = 0\)
Answer: B

Question. If M and N are the points whose coordinates are \((ap^2, 2ap)\) and \((\frac{a}{p^2}, \frac{2a}{p})\) respectively and S is the point (a, 0), then \(\frac{1}{SM} + \frac{1}{SN}\) is equal to _________
(a) a
(b) ap
(c) \(\frac{1}{a}\)
(d) \(\frac{1}{ap}\)
Answer: C

Question. The coordinates of circumcentre of the triangle whose vertices are (3, 6),(4, -4) and (3, -5) are
(a) \(\left(\frac{-3}{2}, 0\right)\)
(b) \(\left(\frac{-3}{2}, \frac{1}{2}\right)\)
(c) \(\left(\frac{1}{2}, -3\right)\)
(d) \(\left(\frac{1}{3}, \frac{3}{2}\right)\)
Answer: B

Question. The ratio in which the line \(2x + 3y - 9 = 0\) divides the points (2, 3) and (4, 7) is _________
(a) 3 : 1
(b) - 5 : 4
(c) - 1 : 5
(d) 2 : 5
Answer: C

Question. The area of a triangle, whose vertices are (a, a - 2), (a + 2, a + 2) and (a + 3, a), is _________
(a) 1 sq unit
(b) 2 sq units
(c) 3 sq units
(d) 4 sq units
Answer: D

Question. If the points (p, 0), (0, q) and (1, 1) are collinear, then \(\frac{1}{p} + \frac{1}{q}\) equals to _______
(a) 1 unit
(b) 2 unit
(c) 3 unit
(d) 4 unit
Answer: A

Question. The distance between the points \((\cos \theta, \sin \theta)\) and \((\sin \theta, \cos \theta)\) is _______
(a) \(\sqrt{3}\)
(b) \(\sqrt{2}\)
(c) 2
(d) 1
Answer: B

Question. If A \(\left(\frac{7}{3}, \frac{m}{5}\right)\) is the midpoint of the line segment joining the points B (3, -2) and C (4, 6), then the value of m is _______
(a) 4
(b) 10
(c) - 4
(d) - 8
Answer: B

Question. If the point A (-3, m) divides the line segment joining the points B (-8, -5) and C (1, - 4) in the ratio a : b, then m equals to
(a) \(-\frac{5}{3}\)
(b) \(\frac{40}{3}\)
(c) \(-\frac{40}{9}\)
(d) \(\frac{30}{7}\)
Answer: C

Question. The ratio, in which the line 5x + 3y = - 9 divides the segment joining the points (2, 3) and (- 3, 4), is ________
(a) 4 : 3
(b) - 4 : 3
(c) - 14 : 5
(d) - 14 : 3
Answer: C

Question. If a point A (-1, 3) divides internally the line segment joining B (3, 4) and C in ratio 2 : 3, then the coordinates of point C is ______
(a) (2,-3)
(b) \(\left(2, \frac{3}{2}\right)\)
(c) \(\left(-1, \frac{3}{2}\right)\)
(d) (-2, 3)
Answer: B

Question. The points (6, 1), (8, 2), (9, 4) and (7, 3) are the vertices of a
(a) trapezium
(b) rectangle
(c) square
(d) rhombus
Answer: D

Question. If the coordinates of mid-point of the sides of a triangle are (21, 7), (- 5, 8) and (10, 8.5), then which among the following is not a vertex of this triangle?
(a) (- 16, 10)
(b) (7, 6)
(c) (36, 7)
(d) (6, 7)
Answer: B

Question. The third vertex of a triangle, if two of its vertices are (- 5, 2) and (1, - 3) and the centroid is at (- 2, 3), is
(a) (- 2, 5)
(b) (- 2, 10)
(c) (0, 5)
(d) (10, - 2)
Answer: B

Question. The vertices of a \(\Delta\) PQR are P (1, 2), Q (- 3, 2) and R (5, - 6). Which among the following is a true statement for this triangle PQR?
(a) Circumcentre of \(\Delta\) PQR is (- 1, - 4)
(b) Circumradius of \(\Delta\) PQR is \(\sqrt{740}\) unit
(c) The point where perpendicular bisectors of PQ and PR intersects, is the circumcentre of the triangle PQR.
(d) All the above
Answer: D

Question. Find the orthecentre of the triangle ABC having its vertices as A (- 2, - 3), B (2, 1) and C (5, - 2).
(a) (- 3, 5)
(b) (- 4, 6)
(c) (2, 1)
(d) (0, 0)
Answer: C

Question. The equation of a line whose inclination is \(60^{\circ}\) and of 5 units on x-axis, is
(a) \(\sqrt{3}x - y = \sqrt{3}\)
(b) \(\sqrt{3}x - y = 5\sqrt{3}\)
(c) \(x - \sqrt{3}y = \sqrt{3}\)
(d) \(x - \sqrt{3}y = 5\sqrt{3}\)
Answer: B

Question. The area of a triangle formed by the line \(4x - 3y + 12 = 0\) with the coordinate axes is __________
(a) 3 sq unit
(b) 4 sq unit
(c) 5 sq unit
(d) 6 sq unit
Answer: D

Question. The equation of a line which is parallel to the line \(3x - 5y + 8 = 0\) and making an intercept - 3 on x-axis is
(a) \(5y - 3x = 9\)
(b) \(5y + 3x = 9\)
(c) \(3x + 5y = 9\)
(d) \(3x - 5y = 9\)
Answer: A

Question. Which among the following can be the vertices of an equilateral triangle?
(a) (2, 3), (5, 4), (7, 8)
(b) (3, - 6), (5,-9), (6, - 12)
(c) \((3,-3), (-3, 3), (-3\sqrt{3}, -3\sqrt{3})\)
(d) All the above
Answer: A

Question. If the vertices of a triangle have integral coordinates, then the triangle cannot be
(a) an equilateral triangle
(b) a right triangle
(c) an isosceles triangle
(d) All the above
Answer: B

Question. If three vertices (in order) of a parallelogram are \((p + q, p - q)\), \((2p + q, 2p - q)\) and \((p - q, p + q)\), then its fourth vertex is _________
(a) \((q, - q)\)
(b) \((2q, - 2q)\)
(c) \((- q, q)\)
(d) \((p, - p)\)
Answer: C

Question. The equation of median drawn from the vertex P to the side QR of a \(\Delta\) PQR, whose vertices are P (2, 3), Q (- 3, - 5) and R (6, 2), is _______.
(a) \(9x - y = 18\)
(b) \(9x - y = 15\)
(c) \(3x - 8y = 18\)
(d) \(3x + 8y = 15\)
Answer: B

Question. A line \(6x + 5y = 30\) intersects the coordinate axes. Find the length of the smallest side of the triangle so formed by the axis.
(a) 3 units
(b) 4 units
(c) 5 units
(d) 6 units
Answer: C

Question. The line segment joining the points (3, - 2) and (4, - 6) is divided by the line \(2x + 3y - 11 = 0\) in the ratio m : n externally at point (a, b). Which among the following is true for the given information?
(a) m = 11
(b) n = 21
(c) \(a - b = \frac{89}{10}\)
(d) All the above
Answer: D

Question. If the mid-points of sides of a \(\Delta\) ABC are P (2, 5), Q (- 3, 8) and R (6, 12), then its vertices are ________
(a) (13, 10), (- 9, 2), (2, 14)
(b) (12, 9), (- 8, 1), (1, 15)
(c) (11, 9), (- 7, 1), (1, 15)
(d) (- 12, 8), (- 7, 2), (- 2, 15)
Answer: C

Question. The three medians of a \(\Delta\) PQR intersect at a point S. If the medians are PM, QN & RT and the area of \(\Delta\) PQR is 90 \(cm^2\), then the area of the quadrilateral MSRN is ________
(a) 45 \(cm^2\)
(b) 30 \(cm^2\)
(c) 15 \(cm^2\)
(d) 60 \(cm^2\)
Answer: B

Question. The length of the side of a square at the vertex of the right angle of Pythagorean triangle of 8 cm, 15 cm and 17 cm the hypotenuse is ________
(a) \(5 \frac{5}{23}\) cm
(b) \(6 \frac{4}{23}\) cm
(c) \(7 \frac{3}{23}\) cm
(d) \(4 \frac{2}{23}\) cm
Answer: A

Question. The length of the diagonal of a square, which can be inscribed in a right triangle of sides 5 cm, 12 cm and 13 cm, is ______
(a) \(\frac{30\sqrt{2}}{17}\) cm
(b) \(\frac{60\sqrt{2}}{17}\) cm
(c) 15 cm
(d) \(10\sqrt{2}\) cm
Answer: B

Question. The equation of a line, which passes through (3, 4) and the product of whose intercepts on the coordinate axes is 48, is _________
(a) \(6x + 9y = 48\)
(b) \(8x + 9y = 48\)
(c) \(4x + 3y = 24\)
(d) \(3x + 4y = 24\)
Answer: C

Question. If the equations of three concurrent lines are \(px + 6y - 8 = 0\), \(qx + 5y - 8 = 0\) and \(rx + 4y - 8 = 0\), then the value of p + r is __________
(a) q
(b) 2q
(c) 3q
(d) 4q
Answer: B

Question. The point (p, q) divides the line formed by joining the points (p + q, p + q) and (p - q, q - p) in the ratio _______
(a) p : q internally
(b) q : p externally
(c) 2 : 1
(d) 1 : 1
Answer: D

Question. The radius of the circle which passes through the origin (0, 0), (0, 6) and (6, 0) is
(a) 12 cm
(b) 6 cm
(c) \(3\sqrt{2}\) cm
(d) \(4\sqrt{2}\) cm
Answer: C

Question. Area of the region formed by the lines \(3|x| + 2|y| = 6\) is
(a) 8 \(cm^2\)
(b) 10 \(cm^2\)
(c) 12 \(cm^2\)
(d) 14 \(cm^2\)
Answer: C

Question. The orthecentre of the triangle formed by the lines \(5x - 8y = 10\), \(16x + 10y = 13\) and y-axis, is _____
(a) \(\left(\frac{102}{89}, \frac{-95}{178}\right)\)
(b) \(\left(\frac{51}{89}, \frac{89}{95}\right)\)
(c) \(\left(\frac{102}{89}, \frac{95}{178}\right)\)
(d) \(\left(\frac{51}{89}, \frac{-95}{89}\right)\)
Answer: A

Question. The line which is perpendicular to \(5x + 2y - 3 = 0\) is _________
(a) \(2x - 5y + 8 = 0\)
(b) \(3x - 5y = 9\)
(c) \(4x - 3y = 7\)
(d) \(5x - 2y = 3\)
Answer: A