Distance Formula

DISTANCE Formula

1) Find the distance between the points

a) (-3, -5) and (-8,7)

b) (4,8) and (4,- 2)

c) (5,2) and (2, 3)

d) (a,0) and (0, b)

e) (-5,3) and (7,8)

2) If the distance between the point P(-3,3) and Q(4,k) be 5√2.

3) show that the point (- 2, - 11) is equidistant from the point (4,6) and (- 3,7).

4) find the coordinates q find the coordinates of the point equidistant from (2,6),(-2,2) and 

(- 5, - 1)

5) Determine the co-ordinate of the middle points of the sides of the triangle whose vertices have co-ordinate (3,2), (-1,-2) & (-5, -4)

6) find the coordinates of the centroid of the triangles whose vertices are

i) (-4,5),(8,2),(2,-1)

ii) (3,4), (-1,7),(10,10)

7) Find the length of the median of the triangle whose vertices are 

(2 - 4), (6 ,- 2) and (- 4,2).

8) prove that the mid-point of the line segment joining the point (2,1) and (6,5) lies on the line joining the points (- 4, - 5) & (9,8).

9) if R (8,17) so that the point of the line segment joining the points (2,1) and (6,5) lies on the line joining the points (-4,-5) and (9,8).

10) Find the coordinates of the vertices of a triangle if the middle point of its side are (2 - 3), (4,2) and (-5,-2)

11) find the lengths of the sides of the triangle whose vertices are 

(-1,5),(3,2),(-1, -1) and show that the triangle is isosceles.

12) show that the points (3,3),(-3,-5) and (- 5 ,- 3) are the vertices of an isosceles triangle.

13) show that the points (3,4),( -1,7) and ( - 3 ,- 4) are the vertices of a right angled triangle.

14) show that the points (1,3),(6,5),(5, - 7) form a right angled triangle

15) show that the points (-1,3),(0,5) and (3,1) are the vertices of a right angled triangle.

16) show that the points (3,3) (-2,- 2) and (8, - 2) are the vertices of of isosceles right angled triangle.

17) The vertices of the triangle are (5,6),(1,2),(9,2). Show that the triangle is right angled and find the area of the triangle.

18) show that the points (-1, 2),(6,-3), (4 ,- 10) and (- 3 ,- 5) are the vertices of a parallelogram.

19) Show that the point (2, 4), (3,8), (5,1),( 4 - 3) are the vertices of a parallelogram.

20) Show that the points (-2 -1),(5,4), (6,7) and (-1,2) are the vertices of a parallelogram.

21) Show that the points (2 - 2),(8,4), (5,7) and (-1,1) are the vertices of a rectangle.

22) Show that the point (2,5),(6,8),(9,12) and (5,9) are the vertices of a rhombus.

23) prove that the points (2,1),(0,0),(-1,2) and (1,3) form a square.