Question

. The area of the triangle ABC with the vertices A(-5, 7), B(-4,-5) and
C(4, 5) is
(a) 63
(b) 35
(c) 53
(d) 36​

Answer 1

Answer:

99m²

Step-by-step explanation:

Area of ∆ = ½ { x1 ( y2 - y3) + x2 (y1 - y2) + x3 ( y3 - y1) }

We know that ,

x1 = -5

x2 = -4

x3 = 4

and

y1 = 7

y2 = -5

y3 = 5

So , area =

½ { -5 (-5-(-5)) + -4 (7-(-5)) + 4 (5 -7)

½ { ( -5 ×10 ) + ( -4 ×35 ) + (4 × -2)

½ (-50) + (-140) + (-8)

½ (-50-140-8)

½ (-198)

-99

But , area of the triangle can't be negative. So, area = 99m²

Answer 2

ANSWER:-

$<bg color=black><font color=blue>$

Area of ΔABC whose vertices are is

$(x_1,y_1),(x_2,y_2) \: and \: (x_3,y_3)are$

$Area \: of ΔABC = \frac{1}{2} [x_1(y_2,y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)]$

In ΔABC, vertices are A(−5,7),B(−4,−5) and C(4,5)

$Area \: of \: triangle \: = \frac{1}{2} (- 5 (- 5 - 5 ) - 4(5 - 7) + 4(7 + 5))$

$= \frac{1}{2} ( - 50 + 8 + 48)$

$= 5 \: sq. \: units$

HOPE IT'S HELPS YOU ❣️