Question

10. In the figure, the curve y = (1 - x)(x + 5) cuts the
x-axis at two points A and B, and the y-axis at the
point C. Find the coordinates of A, B and C.​

Answer 1

Answer:

Given the line,

3x+2y=24⟶(1)

for A putting x=0 in (1),

2y=24

⇒y=12

∴ coordinates of A=(0,12)

for B putting y=0 in (1),

3y=24

⇒x=8

∴ coordinates of B=(8,0)

Midpoint of AB=(

2

8+0

,

2

0+12

)=(4,6)

Now, equation of line perpendicular to line (1),

2x−3y=λ

It will pass through (4,6)

so, 2(4)−3(6)=λ

⇒λ=8−18

⇒λ=−10

Equation of the line parallel to X-axis is,

y=constant

it will pass through (0,−1)

⇒−1=constant

⇒y=−1

To get coordinates of C,putting y=−1 in

2x−3y=−10

⇒2x+3=−10

⇒x=−

2

13

Hence, we have C(−

2

13

,−1),A(0,12)andB(8,0)

∴ Area of $$\triangle ABC

=∣−87−4∣

=∣−91∣

=91squareunits

Answer 2

Answer:

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