Question

1. enrichment given that the points a (5,7), b (8, 2) and c (1, 2) are the vertices of a triangle abc, calculate the length of altitude ah from vertex a to bc.

Explanation:

Step1: Find the equation of line BC

First, find the slope of BC. Points B(8, 2) and C(1, 2). The slope \( m_{BC} = \frac{y_2 - y_1}{x_2 - x_1} = \frac{2 - 2}{1 - 8} = 0 \). So line BC is horizontal, equation is \( y = 2 \).

Step2: Determine the length of altitude AH

The altitude from A(5,7) to BC (y=2) is the vertical distance (since BC is horizontal) between y=7 and y=2. So length \( AH = |7 - 2| = 5 \).

Answer:

5