If the vertex of a triangle is −8,−17   and the midpoints of the sides through it be 2, 1  and −1, 3  , then find the mid-point of the other two sides.

# If the vertex of a triangle is   and the midpoints of the sides through it be  and  , then find the mid-point of the other two sides.

1. A

2. B

3. C

4. D

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### Solution:

Given that, the vertex is (-8, -17).
The midpoints of the sides through it be  and  .
Let the coordinate of other two sides be  .
Let the midpoint of   be (2, 1) and that of   be (-1, 3).
The midpoint between the two points   is given by,

Here,

Since, the midpoint of   is (2, 1), then,
Equating the x-coordinate,

Equating the y-coordinate,
The points are (12, 19).
Since the midpoint of   is (-1, 3).
Here,

Equating x-coordinate,

Equating y-coordinate,

The point is (6, 23).
Find the midpoint of the vertices  .
Substitute the values in the midpoint formula:

The values are  .
Hence, option 3) is correct.

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