# Worksheet on Line-Segment Joining the Points

In math worksheet on line-segment joining the points, we will solve different types of questions.

Recall the formula for the distance between two given points (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

Follow the above formula to solve the below questions given in the worksheet on line-segment joining the points.

1. Find the distance between each of the following pair of points:

(i) (5, 10) and (- 3, 4)

(ii) (- 13, -11) and (-2, - 9)

(iii) ( 2 + √3, 2 - √3) and (- 2 + √3, 2 + √3)

(iv) (x,- y) and ( - x,y)

(v) (a cos θ, a sin θ) and (a cos φ, a sin φ)

(vi) (a + b, c - d) and (a - b, c + d)

(vii) (x + 2, 0) and (0, x - 2)

(viii) (at₁², 2at₁) and (at₂², 2at₁).

2 (i) fir If the distance between the points (x, - 7) and (3, - 3) be 5, find x.

(ii) The distance between the points (7, 3) and (2, y) is √41; find the ordinate of the second point.

(iii) If the distance between the points (p, - 5) and (2, p) be 13 units, find the value of p.

(iv) The square of the distance between the points (- 2, a) and (a, - 3) is 85 find a.

3. (i) Show that the points (2, 2), (- 2, - 2) and (-2√3, 2√3) are the vertices of an equilateral triangle.

(ii) 'Prove that the points (- 1, 5), (3, 2) and (- 1, - 1) are the vertices of an isosceles triangle. Find the co-ordinates of its centroid.

(iii) Show that the points (5, 6), (1, 2) and ( 9, 2) are the vertices of a right-angled triangle ; find its area.

(iv) Prove that the points (7, 9), (3, - 7) and (- 3, 3) form a right-angled isosceles triangle.

4. ABC is an equilateral triangle ; the co-ordinates of the vertices B and C are (2a, 6a) and (2a + √3a, 5a) respectively. Find the co-ordinate of the vertex A.

5. (i) find the point on the x-axis which is equidistant from the points
(2, -1)and(- 3, 4).

(ii) Find the condition so that the point (a, b) may be equidistant from the points (8, 4) and (- 2, - 4).

(iii) If the point (x, y) be equidistant from the points (10, 0), (0, - 10) and (- 8, 6) then prove that x = 0, y = 0.

(iv) Find the co-ordinates of the point which is equidistant from the points (-2, 3), (2, 1) and(5, 3).



6. (1) The co-ordinates of the vertices of a triangle are (0, 0), (5, 3) and (3, 5) respectively ; find the circum-centre and circum-radius of the triangle.

(ii) the co-ordinates of the circum-centre of the triangle ARC are (8, 3) ; if the "co intimates of the vertices A, B and C be (x, -9 ), (y, - 2) and (- 5, 3) respectively , find the values of x and y.

Answers for the worksheet on line-segment joining the points are given below to check the exact answers of the above questions.

1. (i) 10

(ii) 5√5

(iii) 2√7

(iv) 2√(x² + y²)

(v) 2a |sin (θ - φ)/2|

(vi) 2√(b² + d²)

(vii) √[2(x² + 4)]

(viii) a |t₁ - t₂|√(t₁ – t₁)² + 4) units.

2. (i) 6 or, 0

(ii) 7 or, (- 1)

(iii) 7 or (- 10)

(iv) -9 or, 4

3. (ii) (1/3, 2)

(iii) 16 sq. units

4. ( 2a, 4a ) or, ( 2a + √3a, 7a)

5. (i) (- 2, 0)

(ii) 5a + 4b = 15

(iv) (3/2, 5)

6. (i) (17/8, 17/8) and (17√2)/8 units.

(ii) x = 13 or 3 and y = 20 or (-4).

Co-ordinate Geometry