 # Coordinate Geometry Problems with Solutions

Given below are the Class 10 Maths Problems with Solutions for Coordinate Geometry

## Question 1 Prove that the points (a, b + c), (b, c + a) and (c, a + b) are collinear.Solution If the three point are collinear, then Area of the triangle will be zero Area of triangle is given by $A= \frac {1}{2} [x_1(y_2 - y_3) + x_2(y_3 -y_1) + x_3(y_1 - y_2)]$ $A= \frac {1}{2} [a(c+a -a -b) + b(a+b -b -c) + c (b+c - c-a)]$=0$Question 2 For what value of x will the points (x, -1), (2, 1) and (4, 5) lie on a line?Solution If the three point are collinear, then Area of the triangle will be zero Area of triangle is given by$A= \frac {1}{2} [x_1(y_2 - y_3) + x_2(y_3 -y_1) + x_3(y_1 - y_2)]0=\frac {1}{2} [x(1 -5) + 2(5+1) +4(-1-1)]0=-4x +12 -8$x=2 Question 3. Check whether the points (4, 5), (7, 6) and (6, 3) are collinearSolution If the point are collinear, then Area will be zero$A=\frac{1}{2}[4(6-3)+7(3-5)+6(5-6)]=-8$So they are not collinear Question 4. Find the value of q for which the points (7, -2), (5, 1), and (3, q) are collinear.Solution If the point are collinear, then Area must be zero$0=\frac{1}{2}[7(1-q)+5(q+2)+3(-2-1)]$q=4 ## Long Asnwer type Question 1. Find a point on the y – axis which is equidistant from the point A (6, 5) and B (-4, 3). Question 2. Show that the points (p, p), (-p, -p) and (-p3, p3) are the vertices of an equilateral triangle. Also find its area. Question 3. Show that four points (0, -1), (6, 7), (-2, 3) and (8, 3) are the vertices of a rectangle. Also find its area. Question 4. If two vertices of an equilateral triangle be (0,0), (3, 3), find the third vertex. Question 5. If P (2, -1), Q (3, 4), R (-2, 3) and S (-3, -2) be four points is a plane, show that PQRS is a rhombus but not a square. Find the area of the rhombus. Question 6. Show that the points (-4, -1), (-2, -4), (4, 0) and (2, 3) are the vertices points of a rectangle. Question 7. Show that the points A (1, -2), B (3, 6), C (5, 10) and D (3, 2) are the vertices of a parallelogram. Question 8. Prove that the points A (1, 7), B (4, 2), C (-1, -1) and D (-4, 4) are the vertices of a square. Question 9. Prove that the points (3, 0), (6, 4) and (-1, 3) are vertices of a right angled isosceles triangle. Question 10. Find the circumcenter of the triangle whose vertices are (-2, -3), (-1, 0), (7, -6) Question 11. If two opposite vertices of a square are (5, 4) and (1, -6), find the co- ordinates of its remaining two vertices. Question 12. Show that the points A (5, 6), B (1, 5), C (2, 1) and D (6, 2) are the vertices of a square. Question 13 If the points (p, q) (m, n) and (p - m, q -n) are collinear, show that pn = qm. Question 14 Find k so tht the point P (-4, 6) lies on the line segment joining A (k, 10) and B (3, -8). Also, find the ratio in which P divides AB. Question 15 Find the area of the quadrilaterals, the co- ordinates of whose vertices are (i)(-3, 2), (5, 4), (7, -6) and (-5, -4) (ii)(1, 2), (6, 2), (5, 3) and (3, 4) (iii) (-4, -2), (-3, -5), (3, -2), (2, 3) Question 16 Show that the following sets of points are collinear (i) (2, 5), (4, 6) and (8, 8) (ii) (1, -1), (2, 1) and (4, 5) Question 17. Find the value of x such that PQ = QR where the co- ordinates of P, Q and R are (6, -1), (1, 3) and (x, 8) respectively. link to this page by copying the following text Also Read Go back to Class 10 Main Page using below links ### Practice Question Question 1 What is$1 - \sqrt {3}\$ ?
A) Non terminating repeating
B) Non terminating non repeating
C) Terminating
D) None of the above
Question 2 The volume of the largest right circular cone that can be cut out from a cube of edge 4.2 cm is?
A) 19.4 cm3
B) 12 cm3
C) 78.6 cm3
D) 58.2 cm3
Question 3 The sum of the first three terms of an AP is 33. If the product of the first and the third term exceeds the second term by 29, the AP is ?
A) 2 ,21,11
B) 1,10,19
C) -1 ,8,17
D) 2 ,11,20