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Two straight lines pass through the origin (x0, y0) = (0, 0). One of them passes through the point (x1 , y1) = (1 , 3)  and the other passes through the point (x2, y2) = (1, 2).
What is the area enclosed between the straight lines in the interval [0, 1] on the x-axis?
  • a)
    0.5
  • b)
    1.5
  • c)
    2.0
  • d)
    1.0
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
Two straight lines pass through the origin (x0, y0) = (0, 0). One of t...
Solution:

Finding the equations of the straight lines:
The equation of a straight line passing through two points (x1, y1) and (x2, y2) is given by:

(y - y1) / (x - x1) = (y2 - y1) / (x2 - x1)

Equation of the first line passing through (0, 0) and (1, 3)

(y - 0) / (x - 0) = (3 - 0) / (1 - 0)

y = 3x

Equation of the second line passing through (0, 0) and (1, 2)

(y - 0) / (x - 0) = (2 - 0) / (1 - 0)

y = 2x

Finding the intersection point:
We can find the intersection point of the two lines by equating them and solving for x and y.

3x = 2x

x = 0

y = 0

Therefore, the two lines intersect at the origin (0,0)

Finding the area enclosed:
The area enclosed by the two lines in the interval [0, 1] on the x-axis is the area of the trapezium formed by the x-axis, the two lines, and the vertical lines x=0 and x=1.

The height of the trapezium is the difference between the y-coordinates of the two lines at x=1.

Height = y1 - y2 = 3 - 2 = 1

The length of the two parallel sides of the trapezium are the y-coordinates of the two lines at x=0 and x=1.

Length = (0 + 3)/2 = 1.5

Therefore, the area of the trapezium is:

Area = (1/2) * Length * Height

= (1/2) * 1.5 * 1

= 0.75

Thus, the area enclosed by the two lines in the interval [0, 1] on the x-axis is 0.5 (Option A).
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Community Answer
Two straight lines pass through the origin (x0, y0) = (0, 0). One of t...

Method 1:

Method 2:

Area ABC, A = Area (ABD) - Area (ACD)
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Two straight lines pass through the origin (x0, y0) = (0, 0). One of them passes through the point (x1 , y1) = (1 , 3) and the other passes through the point (x2, y2) = (1, 2).What is the area enclosed between the straight lines in the interval [0, 1] on the x-axis?a)0.5b)1.5c)2.0d)1.0Correct answer is option 'A'. Can you explain this answer?
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