Question

Finding the area of a triangle is straightforward if you know the length of the base and the height of the triangle. But is it possible to find the area of a triangle if you know only the coordinates of its vertices? In this task, you’ll find out. Consider ΔABC, whose vertices are A(2, 1), B(3, 3), and C(1, 6); let line segment AC represent the base of the triangle.

Part A
Find the equation of the line passing through B and perpendicular to .

Answer 1

y = x/5 + 12/5

Explanation:

Slope of AC is (6 - 1)/(1 - 2) = -5

slope of the line perpendicular to AC is -1//(-5) = 1/5

the equation of the line perpendicular to AC is y = x/5 + b

the equation of the line passing through B, so 3 = 3/5 + b, b = 12/5

the equation of the line passing through B and perpendicular to AC is y = x/5 + 12/5