 # Coordinate Geometry Problems with Solutions

Given below are the Class 10 Maths Problems with Solutions for Coordinate Geometry
(a) Concepts questions
(b) Calculation problems

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.
Check whether the points (4, 5), (7, 6) and (6, 3) are collinear

Question 4.
Find the value of q for which the points (7, -2), (5, 1), and (3, q) are collinear.

Question 5.
Show that four points (0, -1), (6, 7), (-2, 3) and (8, 3) are the vertices of a rectangle. Also find its area.

Question 6.
If two vertices of an equilateral triangle be (0,0), (3, 3), find the third vertex.

Question 7.
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 8.
Show that the points (-4, -1), (-2, -4), (4, 0) and (2, 3) are the vertices points of a rectangle.

Question 9.
Show that the points A (1, -2), B (3, 6), C (5, 10) and D (3, 2) are the vertices of a parallelogram.

Question 10.
Prove that the points A (1, 7), B (4, 2), C (-1, -1) and D (-4, 4) are the vertices of a square.

Question 11.
Prove that the points (3, 0), (6, 4) and (-1, 3) are vertices of a right angled isosceles triangle.

Question 12.
Find the circumcenter of the triangle whose vertices are (-2, -3), (-1, 0), (7, -6)

Question 13.
If two opposite vertices of a square are (5, 4) and (1, -6), find the co- ordinates of its remaining two vertices.

Question 14.
Show that the points A (5, 6), B (1, 5), C (2, 1) and D (6, 2) are the vertices of a square.

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### 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

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