The coordinates of the vertex of the triangle A (-2; 4), B (-6; 8), C (5; -6) are given. Find: the lengths of the sides and determine

| May 4, 2021 | education

The coordinates of the vertex of the triangle A (-2; 4), B (-6; 8), C (5; -6) are given. Find: the lengths of the sides and determine the shape of the triangle by the angles, the length of the median BM, the height CH of the bisector AD.

To find the length of the segment AB, given by the coordinates of the ends, use the formula:

| AB | = √ (| Ax – Bx | ^ 2 + | Ay – By | ^ 2).

Substitute the coordinates of the ends of the side of the triangle into this formula:

| AB | = √ (| -2 + 6 | ^ 2 + | 4 – 8 | ^ 2) = √ (16 + 16) = 4√2.

| AC | = √ (| -2 – 5 | ^ 2 + | 4 + 6 | ^ 2) = √ (49 + 100) = √149.

| BC | = √ (| -6 – 5 | ^ 2 + | 8 + 6 | ^ 2) = √ (121 + 196) = √317.

The sides of the triangle are of different lengths, so the triangle is versatile.

The middle of the M side has coordinates Mx = Ax – Cx = -2 – 5 = -7, My = Ay – BY = 4 + 6 = 10. The median BM will have the length: | BM | = √ (| -6 + 5 | ^ 2 + | 8 – 10 ^ 2) = √ (1 + 4) = √5.



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