Question

type the correct answer in each box. use numerals instead of words. if necessary, use / for the fraction bar(s).
triangle abc is defined by the points a(3,8), b(7,5), and c(2,3).
create an equation for a line passing through point a and perpendicular to bc.

Explanation:

Step1: Calculate the slope of line \(BC\)

The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). For points \(B(7,5)\) and \(C(2,3)\), \(m_{BC}=\frac{5 - 3}{7 - 2}=\frac{2}{5}\).

Step2: Find the slope of the line perpendicular to \(BC\)

If two lines are perpendicular, the product of their slopes is \(- 1\). Let \(m\) be the slope of the line perpendicular to \(BC\). Then \(m\times\frac{2}{5}=-1\), so \(m =-\frac{5}{2}\).

Step3: Use the point - slope form to find the equation of the line

The point - slope form is \(y - y_1=m(x - x_1)\). Using point \(A(3,8)\) and \(m =-\frac{5}{2}\), we have \(y - 8=-\frac{5}{2}(x - 3)\).

Step4: Simplify the equation

$$
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$$

Answer:

\(y =-\frac{5}{2}x+\frac{31}{2}\)