In math worksheet on linesegment 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 coordinate points and the different types of examples Click Here.
Follow the above formula to solve the below questions given in the worksheet on linesegment 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 coordinates of its centroid.
(iii) Show that the points (5, 6), (1, 2) and ( 9, 2) are the vertices of a rightangled triangle ; find its area.
(iv) Prove that the points (7, 9), (3,  7) and ( 3, 3) form a rightangled isosceles triangle.
4. ABC is an equilateral triangle ; the coordinates of the vertices B and C are (2a, 6a) and (2a + √3a, 5a) respectively. Find the coordinate of the vertex A.
5. (i) find the point on the xaxis 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 coordinates of the point which is equidistant from the points (2, 3), (2, 1) and(5, 3).
`6. (1) The coordinates of the vertices of a triangle are (0, 0), (5, 3) and (3, 5) respectively ; find the circumcentre and circumradius of the triangle.
(ii) the coordinates of the circumcentre 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 linesegment 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).
● Coordinate Geometry
11 and 12 Grade Math
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