Question

The straight line L has equation 5x + 2y = 31

The point A has coordinates (0, 1)
The straight line M is perpendicular to L and passes through A.
Line L crosses the y-axis at the point B.
Lines L and M intersect at the point C.
Work out the area of triangle ABC.
You must show all your working.

Answer 1

Area of ∆ABC =

Draw the lines and points to create the triangle, use the distance formula to get the side lengths, and then use herons formula by taking the square root of the semi-perimeter multiplied by the difference of each side and the semi- perimeter.

Explanation:

Area of ∆ABC =

Draw the lines and points to create the triangle, use the distance formula to get the side lengths, and then use herons formula by taking the square root of the semi-perimeter multiplied by the difference of each side and the semi- perimeter.

Answer 2

Area of ∆ABC =
`\boxed{(145)/(4) \: units}`

Draw the lines and points to create the triangle, use the distance formula to get the side lengths, and then use herons formula by taking the square root of the semi-perimeter multiplied by the difference of each side and the semi- perimeter.