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It looks like AB has a slope of 1/2 and BC has a slope of -2.

These two slopes are negative reciprocals of each other, meaning their product is -1. This also means that AB is perpendicular to BC.

The equation of the line containg A(-1, -2) and B(2, 2) is found by using the slope-intercept form of the linear equation ( ), and either point A or B. I'll use A. Substituting, we have

To translate the equation into the general form Ax + By + C = 0, first multiply each term by 2 to eliminate the denominator:

Then, transpose (move) the 2y to the right side of the equation. Don't forget to change its sign.

Finally, use the symmetric property of equality to get:

You can follow these steps to define the equation of the perpendicular that passes through points B and C. Just remember to use the gradient (slope) of -2 and either point B or C.

Good Luck!