Q13 of 112 Page 156

A triangle has vertices at (6, 7), (2, –9) and (–4, 1). Find the slopes of its medians.

Given: Vertices of triangle A (6, 7), B (2, –9) and C (–4, 1)


To find the slopes of medians. We need to know the mid–points of AB, BC and AC.


D, E and F are mid–points of AB, BC and AC respectively.



Mid – point formula =


Mid – point of AB =





Mid – point of BC =





Mid – point of AC =




F = (1, 4)


Slopes of median of triangles:


Slope of line passing through (x1, y1) and (x2, y2) is



A (6, 7) and E (–1, –4)


Slope of AE




B (2, –9) and E (1, 4)


Slope of BF




C (–4, 1) and D (4, –1)


Slope of CD




More from this chapter

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11

The line joining the points A (0, 5) and B (4, 2) is perpendicular to the line joining the points C (–1, –2) and D (5, b). Find the value of b.

 12

The vertices of ΔABC are A (1, 8), B (–2, 4), C (8, –5). If M and N are the midpoints of AB and AC respectively, find the slope of MN and hence verify that MN is parallel to BC.

14

The vertices of a ΔABC are A (–5, 7), B (–4, –5) and C (4, 5). Find the slopes of the altitudes of the triangle.

 15

Using the concept of slope, show that the vertices (1, 2), (–2, 2), (–4, –3) and (–1, –3) taken in order form a parallelogram.