# Worksheet on Distance Between Two Points

In math worksheet on distance between two points, students can practice different types of questions in this sheet.

#### Recall the formula to find the distance between two Cartesian co-ordinates (rectangular co-ordinates):

(x₁, y₁) and (x₂, y₂) is

√{(x₂ - x₁)² + (y₂ - y₁)²}.

To know more about the distance between the two or more co-ordinate 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 co-ordinates 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 co-ordinates 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 line-segment joining the points (7, -1) and (9, 3) ; if the abscissa of the vertex be 4, find its ordinate.

7. The co-ordinates 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 co-ordinates 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.

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 )

Co-ordinate Geometry

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