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Worksheet on Distance Between Two Points
Recall the formula to find the distance between two Cartesian coordinates (rectangular coordinates):(x_{1}, y_{1}) and (x_{2}, y_{2}) isTo know more about the distance between the two or more coordinate points and the different types of examples Click Here. Using the above formula to solve the below questions given in the worksheet on distance between two points. 1. The coordinates of the points A and B are (2, 4) and (2, 6) respectively. The point P is on that side of AB opposite to the origin. If PAB be an equilateral triangle, find the coordinates of P. 2. (i) Prove that the points (2,  2), (8, 4), (5, 7) and ( 1, 1) are the vertices of a rectangle ; find the area of the rectangle. (ii) Show that the points ( 2,  1), (5, 4), (6, 7) and (1, 2) are the vertices of a parallelogram. Is the parallelogram a rectangle ? (iii) Prove that the four points (2, 6), (5, 1), (0,  2) and ( 3, 3) are the vertices of a square ; find the area of the square formed. (iv) Prove that the points (0, 0), (0, 10), (8, 16) and (8, 6) are the vertices of a rhombus ; find the area of the rhombus. Show also that the diagonals of the rhombus intersect at right angles. 3. Prove that the circle having centre at (4, 3) passes through the points (0, 0), (8, 0), (1, 7) and (1,  1) ; find the radius of the circle. 4. The centre of a circle is at (5, 3) and its radius is 5. Find the length of the chord which is bisected at (3, 2). 5. If the point (x, y) be equidistant from the points (a + b, b  a) and (a  b, a + b), prove that bx = ay. 6. The base of an isosceles triangle is the linesegment joining the points (7, 1) and (9, 3) ; if the abscissa of the vertex be 4, find its ordinate. 7. The coordinates of the points A, B, C are respectively ( 2, 1), ( 1,  3) and (3,  2). Show that, AB = BC and angle ABC is a right angle. If D is the fourth vertex of the square ABCD, find the coordinates of D and find the point of intersection of diagonals of ABCD. Answers for the worksheet on distance between two points are given below to check the exact answers of the above questions. Answers:1. (2 + √3a, 5)2. (i) 36 sq. units (ii) No (iii) 34 sq. units (iv) 80 sq. units. 3. 5 units. 4. 4√5 units. 6. 3 7. (2, 2) and (1/2, 1/2 ) ● Coordinate Geometry
11 and 12 Grade Math


