if the coordinates of the midpoint side of a triangle are (5,7);(4,6);(3,4) find it vertices
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Answer:
Let the vertices of triangle be (x
1
,y
1
),(x
2
,y
2
) and (x
3
,y
3
).
By using the given information in the question,
2
x
1
+x
2
=3
⇒x
1
+x
2
=6…(1)
Similarly,
x
2
+x
3
=8…(2)
x
3
+x
1
=10…(3)
By using equation (1),
x
2
=6−x
1
Substitute the above value of x
2
in equation (2)
6−x
1
+x
3
=8
⇒x
3
−x
1
=2…(4)
Add equations (4) and (3),
2x
3
=12
∴x
3
=6
And,
x
1
=4(from4)
x
2
=6−x
1
=6−4
=2
By using the same method value of y
1
=5,y
2
=3 and y
3
=9 are calculated.
Vertices of triangle are (4,5),(2,3),(6,9).
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