Question

Find the third vertex of a triangle if its two vertices are (-1,4) and (5,2) and the mid-point of one side is (0,3)..

Answer 1

Answer:

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)