WHAT will be the area of a triangle formed by straight line y=mx+c with coordinate axes??

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Answer

Area of a triangle formed by a straight line with coordinate axes

When a straight line intersects the x and y axes, it forms a triangle with the coordinate axes. To find the area of this triangle, we need to follow the following steps:

Step 1: Find the coordinates of the points where the line intersects the axes

To find the coordinates of the points where the line intersects the axes, we need to substitute x = 0 and y = 0 into the equation of the line y = mx + c. This gives us:

When x = 0, y = c

When y = 0, x = -c/m

Step 2: Calculate the length of the base of the triangle

The length of the base of the triangle is the distance between the x-intercept and the y-intercept. We can use the distance formula to calculate this:

d = sqrt((0 - (-c/m))^2 + (c - 0)^2)

Simplifying this gives us:

d = sqrt(c^2/m^2 + c^2)

d = c sqrt(1/m^2 + 1)

Step 3: Calculate the height of the triangle

The height of the triangle is the y-coordinate of one of the points where the line intersects the axes. We can use the equation of the line to find this:

h = mc + c

h = c(m + 1)

Step 4: Calculate the area of the triangle

The area of the triangle is given by the formula:

A = 1/2 * base * height

Substituting the values we calculated earlier, we get:

A = 1/2 * c sqrt(1/m^2 + 1) * c(m + 1)

Simplifying this gives us:

A = 1/2 * c^2 * sqrt(1/m^2 + 1) * (m + 1)

Therefore, the area of the triangle formed by the straight line y = mx + c with the coordinate axes is:

A = 1/2 * c^2 * sqrt(1/m^2 + 1) * (m + 1)

Answer

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