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 AABC, whose vertices are A (2,1), B (3, 3), and C (1,6) ; let AC represent the base of the triangle. Part A Find the equation of the line passing through B and perpendicular to AC.

Answer 1

Answer: y = x/5 + 12/5

Step-by-step explanation:

The first step is to find the equation of line AC

The equation of a line in the slope intercept form is expressed as

y = mx + c

where

m represents slope

c represents y intercept.

The formula for calculating slope of a line is expressed as

m = (y2 - y1)/(x2 - x1)

Considering line AC with points, A(2, 1) and C(1, 6),

x1 = 2, y1 = 1

x2 = 1, y2 = 6

m = (6 - 1)/(1 - 2) = 5/- 1 = - 5

Recall, if two lines are perpendicular, it means that the slope of one line is the negative reciprocal of the slope of the other line. Negative reciprocal of - 5 is 1/5

Thus, slope of the perpendicular line passing through B(3, 3) is m = 1/5

We would find the y intercept, c of the line by substituting m = 1/5, x = 3 and y = 3 into the slope intercept equation. We have

3 = 1/5 * 3 + c

3 = 3/5 + c

c = 3 - 3/5

c = 12/5

By substituting m = 1/5 and c = 12/5 into the slope intercept equation, the equation of the line is

y = x/5 + 12/5