Question

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

Answer 1

Formula: 1 Mark
Steps: 2 Marks
Answer: 1 Mark

Let the third vertex be (x, y)
Using mid-point formula, we have
$\frac{x+5}{2}=0\Rightarrow x=-5$
and $\frac{y+2}{2}=3\Rightarrow y=4$
or
$\frac{x-1}{2}=0\Rightarrow x=1,$
$\frac{y+4}{2}=3\Rightarrow y=2$

(0,3) can be the midpoint of either side. So we are getting two values of the vertex of the third side.
Hence, third vertex is (-5, 4) or (1,2)