Question

9. Find the area of the triangle formed by the lines 4x + y - 16 = 0, x - y + 1 = 0 and x-6 y -4=0 ​

Answer 1

Answer:

MATHS

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Asked on November 22, 2019 by

Jeeva Pawar

Find the area of the triangle formed by the straight lines whose equations are

y=x,y=2x, and y=3x+4.

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ANSWER

y=x.....(i)

y=2x......(ii)

y=3x+4......(iii)

Solving (i) and (ii)

⇒x=0,y=0

So the point of intersection is A(0,0)

solving (ii) and (iii)

⇒x=−4,y=−8

so the second point of intersection is B(−4,−8)

solving (i) and (iii)

⇒x=−2,y=−2

so the third point of intersection is C(−2,−2)

So the vertices of triangle are A(0,0),B(−4,−8) and (−2,−2)

Area of triangle =△=

2

1

∣

∣

∣

∣

∣

∣

∣

∣

0

−4

−2

0

−8

−2

1

1

1

∣

∣

∣

∣

∣

∣

∣

∣

△=

2

1

{0(−8×1−1×−2)−0(−4×1−1×−2)+1(−4×−2−)−(−4)×−8)}

△=

2

1

∣−8∣

△=4