Understanding Perpendicular Lines: Slopes and 90-Degree Intersections in Math

Perpendicular

Perpendicular lines are lines that intersect at a right angle, forming a 90-degree angle

Perpendicular lines are lines that intersect at a right angle, forming a 90-degree angle. In other words, if two lines are perpendicular, they form an “L” shape when they meet.

To determine if two lines are perpendicular, you need to look at their slopes. The slope of a line represents how steep it is. If the slopes of two lines are negative reciprocals of each other, then the lines are perpendicular.

The formula to find the slope (m) between two points (x1, y1) and (x2, y2) is given by:

m = (y2 – y1) / (x2 – x1)

For example, let’s say we have two points A(2, 3) and B(4, -5). We can calculate the slope of the line passing through these two points:

m = (-5 – 3) / (4 – 2) = -8 / 2 = -4

Now, let’s have another line passing through point C(1, 2) with a slope m = 1/4. We can calculate the slope of this line using the same formula:

m’ = (y2 – y1) / (x2 – x1) = (2 – 2) / (1 – 1) = 0 / 0

In this case, we cannot determine the slope because we have a division by zero. However, we can still determine if the lines are perpendicular by looking at the slopes.

Since the slope of line AB is -4 and the slope of line AC is undefined, we cannot compare the slopes to determine perpendicularity. But, by visual inspection, we can see that the lines AB and AC are indeed perpendicular as they intersect at a right angle.

In summary, to determine perpendicularity between two lines, you need to either calculate the slopes and check if they are negative reciprocals or visually inspect if the lines form a 90-degree angle.

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