Q29 of 149 Page 14

Find the lengths of the medians of a ABC having vertices at A (5, 1), B (1, 5), and C(-3, -1).

Here given vertices are A (0,-1), B (2, 1) and C (0, 3) and let midpoints of BC, CA and AB be D,E and F respectively.



By midpoint formula.


x = , y =


For midpoint D of side BC,


x = , y =


x = , y =


∴midpoint of side BC is D(-1, 2)


For midpoint E of side AB,


x = , y =


x = , y =


∴midpoint of side AB is E(1, 0)


For midpoint F of side CA,


x = , y =


x = , y =


∴midpoint of side CA is F(3, 3)


By distance formula,


XY =


For median AD,


AD =


=


= units


For median BE,


BE =


=


= 5 units.


For median CF,


CF =


=


= units


More from this chapter

All 149 →
27

If the coordinates of the mid-points of the sides of a triangle be (3, -2), (-3, 1) and (4, -3), then find the coordinates of its vertices.

 28

Find the lengths of the medians of a ABC having vertices at A (0,-1), B (2, 1) and C (0, 3).

 30

Find the coordinates of the points which divide the line segment joining the points (-4, 0) and (0, 6) in four equal parts.

 31

Show that the mid-point of the line segment joining the points (5, 7) and (3, 9) is also the mid-point of the line segment joining the points (8, 6) and (0, 10).