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?
slopes of parallel lines are equal.
slopes of perpendicular lines are
negative reciprocals.
What do you think?
To determine whether the lines AB and AC are parallel, perpendicular, or neither, we need to compare their slopes.
Let's start by finding the slope of AB. The slope of a line passing through two points (x1, y1) and (x2, y2) is given by the formula:
slope = (y2 - y1) / (x2 - x1)
In this case, the coordinates of point A are (2, 5) and the coordinates of point B are (8, 1). Let's calculate the slope of AB:
slope_AB = (1 - 5) / (8 - 2) = -4 / 6 = -2 / 3
Now, let's find the slope of AC. The coordinates of point A are (2, 5), and the coordinates of point C are (-2, -1). Let's calculate the slope of AC:
slope_AC = (-1 - 5) / (-2 - 2) = -6 / -4 = 3 / 2
Comparing the slopes, we find that the slope of AB (-2/3) is the negative reciprocal of the slope of AC (3/2). Two lines are perpendicular when their slopes are negative reciprocals of each other. Therefore, lines AB and AC are perpendicular to each other.