Find the area of $△$ le with coordinate of vertices $A (- 5, - 1), B (3, - 5)$ and $C (5, 2)$ resp. Find the length of median trough $B$ .

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Solution

$A (- 5, - 1), B (3, - 5) C (5, 2)$

Area of $Δ A B C$ = $\frac{1}{2} [x_{1} (y_{2} - y_{3}) + x_{2} (y_{3} - y_{1}) + x_{3} (y_{1} - y_{2})]$

$= \frac{1}{2} [- 5 (- 5 - 2) + 3 (2 + 1) + 5 (- 1 + 5)]$

$= \frac{1}{2} [- 5 \times - 7 + 3 \times 3 + 5 \times 4]$

$= \frac{1}{2} [35 + 9 + 20]$

$= \frac{1}{2} [64]$

$= 32 s q u n i t s$

Mid point of AC=

$(\frac{- 5 + 5}{2}, \frac{- 1 + 2}{2}) = (0, \frac{1}{2})$

Length of Median through B= $B = \sqrt{{(3 - 0)}^{2} + {(- 5 \frac{- 1}{2})}^{2}}$

$= \sqrt{9 + \frac{121}{4}}$

$= \frac{\sqrt{157}}{2} u n i t$

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Find the area of △ le with coordinate of vertices A(−5,−1),B(3,−5) and C(5,2) resp. Find the length of median trough B.

A(−5,−1),B(3,−5)C(5,2) Area of ΔABC=12[x1(y2−y3)+x2(y3−y1)+x3(y1−y2)] =12[−5(−5−2)+3(2+1)+5(−1+5)] =12[−5×−7+3×3+5×4] =12[35+9+20] =12[64] =32squnits Mid point of AC= (−5+52,−1+22)=(0,12) Length of Median through B=B=√(3−0)2+(−5−12)2 =√9+1214 =√1572unit

Find the area of $△$ le with coordinate of vertices $A (- 5, - 1), B (3, - 5)$ and $C (5, 2)$ resp. Find the length of median trough $B$ .