Triangle ΔABC has vertices A(2,5), B(8,1) and C(-2,-1) and is a right triangle. If the slope of AB is -2/3 and the slope of AC is 3/2, are the lines parallel, perpendicular or neither?

i was thinking neither..im not sure though

If two lines are perpendicular, then their slopes are negative reciprocals of each other, or another way of looking at it, when their slopes are multiplied the result is -1

Is (-2/3)(3/2) = -1 ???

yes

To determine if the lines AB and AC are parallel, perpendicular, or neither, we need to compare their slopes.

The slope of a line is given by the formula:

slope = (change in y) / (change in x)

For line AB, with points A(2,5) and B(8,1), we can calculate the slope using the formula:

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

slope_AB = (1 - 5) / (8 - 2) = -4 / 6 = -2 / 3

Similarly, for line AC, with points A(2,5) and C(-2,-1), we can calculate the slope using the formula:

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

slope_AC = (-1 - 5) / (-2 - 2) = -6 / -4 = 3 / 2

Now, we compare the slopes:

If the product of the slopes is -1 (negative reciprocals), then the lines are perpendicular.
If the slopes are equal, then the lines are parallel.
If neither of these conditions is met, then the lines are neither parallel nor perpendicular.

Let's calculate the product of the slopes:

slope_AB * slope_AC = (-2 / 3) * (3 / 2) = -6 / 6 = -1

Since the product of the slopes is -1, the lines AB and AC are perpendicular to each other.