if line segment bc is considered the base of triangle abc, what is the corresponding height of the triangle…

Explanation:

Step1: Identify the base - line segment BC

The line segment BC is on the grid. We can find the length of BC using the distance formula for two - dimensional points or by counting grid units. Points B(3, 2) and C(-1,-1).

Step2: Determine the perpendicular distance from A to BC

The perpendicular distance from point A(-1, 1) to the line segment BC is the height of the triangle with base BC. We can use the fact that the height is the vertical distance from point A to the line containing BC. The y - coordinate of point A is 1. The equation of the line passing through B(3,2) and C(-1,-1) has a slope $m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{2+1}{3 + 1}=\frac{3}{4}$. The equation of the line BC using the point - slope form $y - y_1=m(x - x_1)$ with point C(-1,-1) is $y+1=\frac{3}{4}(x + 1)$ or $y=\frac{3}{4}x-\frac{1}{4}$. The perpendicular distance from point A(-1,1) to the line $y=\frac{3}{4}x-\frac{1}{4}$ can also be found by counting the vertical grid - units. Counting the vertical distance from point A to the line segment BC, we find that the height is 1.6 units.

Answer:

1.6 units