find the third vertex of a triangle if two of its vertices are at (-1,4) and (5,2) and the medians meet at (0,-3)
Answers
We know that A(−1,4),B(0,3) which is
given C(5,2)
Let the third vertex (x
1
,y
1
). There are two join case
we join vertex (x
1
,y
1
) with (−1,4) mid of this segment is (0,3) then
Using mid value formula
2
x
1
+x
2
=0,
2
y
1
+y
2
=3
x
1
+x
2
=0,y
1
+y
2
=6
x
1
=−x
2
,y
1
=6−y
2
x
1
=1,y
1
=6−4=2
(x
1
,y
1
)=(1,2)
i.e third vertex D(1,2)=(x
1
,y
1
)
E(x
1
′
,y
1
′
) join with C(5,2) vertex and mid point (0,3)
Now we can write D(0,3) is mid point of line segment between (x
1
′
,y
1
′
) and (5,2)
2
x
1
′
+5
=0,
2
y
1
′
+2
=3
x
1
′
=−5, y_{1}'=4$$
(x
1
′
,y
1
′
)=(−5,4)
another vertex (−5,4)E
The required vertex could be either (5,4) and (1,2)
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Answer:
find the third vertex of a triangle if two of its vertices are at (-1,4) and (5,2) and the medians meet at (0,-3)