Q20 of 48 Page 102

Prove that the mid–point of the line segment joining the points (5, 7) and (3, 9) is the same as the mid–point the line segment joining the points (8, 6) and (0, 10).

Using mid–point formula:


Coordinates of the mid–point of the line segment joining the points (5, 7) and (3, 9) are


= (4, 8)


and


Coordinates of the mid–point of the line segment joining the points (8, 6) and (0, 10) are


= (4, 8)


Hence proved that the mid–point of the line segment joining the points (5, 7) and (3, 9) is the same as the mid–point the line segment joining the points (8, 6) and (0, 10).


More from this chapter

All 48 →
17

There are four points P(2, –1), Q(3, 4), R(–2, 3) and S(–3, –2) in a plane. Then prove that PQRS in not a square, rather it is a rhombus.

 18

Prove that the mid–point C of the hypotenuse in a right angled triangle AOB is situated at equal distances from the vertices O, A and B of the triangle.

 19

Find the length of medians of the triangle whose vertices are (1, –1), (0, 4) and (–5, 3).

 21

If the mid–points of the sides of a triangle are (1, 2), (0, –1) and (2, –1), then find the coordinates of the vertices of the triangle.