Question -
Answer -
Given:
3x + 2y + 6 = 0 … (1)
2x − 5y + 4 = 0 … (2)
x − 3y − 6 = 0 … (3)
Let us assume, intriangle ABC, let equations (1), (2) and (3) represent the sides AB, BC and CA,respectively.
Solving equations (1)and (2), we get
x = −2, y = 0
Thus, AB and BCintersect at B (−2, 0).
Now, solving (1) and(3), we get
x = – 6/11, y = –24/11
Thus, AB and CAintersect at A (-6/11, -24/11)
Similarly, solving (2)and (3), we get
x = −42, y = −16
Thus, BC and CAintersect at C (−42, −16).
Now, let D, E and F bethe midpoints the sides BC, CA and AB, respectively.
Then, we have:
∴ The equations ofthe medians of a triangle are: 41x – 112y – 70 = 0,
16x – 59y – 120 = 0,25x – 53y + 50 = 0