Are the lines that goes through the points given below perpendicular? How do you know
Line 1 goes through (-5,0) and (-3,-3)
LIne 2 goes through (4,2) and (-2, -2)
To determine if the lines that go through the given points are perpendicular, we can calculate the slopes of the lines.
The slope of a line passing through points (x1, y1) and (x2, y2) can be calculated using the formula: slope = (y2 - y1) / (x2 - x1).
For Line 1, the points are (-5,0) and (-3,-3). The slope of Line 1 is: (0 - (-3)) / (-5 - (-3)) = 3 / (-2) = -1.5.
For Line 2, the points are (4,2) and (-2,-2). The slope of Line 2 is: (2 - (-2)) / (4 - (-2)) = 4 / 6 = 2 / 3.
Two lines are perpendicular to each other if the product of their slopes is -1. In this case, the product of the slopes is (-1.5) * (2 / 3) = -1. Therefore, the lines that go through the given points are perpendicular.
To determine if two lines are perpendicular, we need to check the slopes of the lines. If the slopes are negative reciprocals of each other, then the lines are perpendicular.
Here's how to find the slopes and determine if the lines are perpendicular:
For Line 1:
1. Identify the coordinates of the two points: (-5,0) and (-3,-3).
2. Calculate the slope using the formula: slope = (y2 - y1) / (x2 - x1).
- For Line 1, the slope is: (-3 - 0) / (-3 - (-5)) = -3 / 2
For Line 2:
1. Identify the coordinates of the two points: (4,2) and (-2,-2).
2. Calculate the slope using the formula: slope = (y2 - y1) / (x2 - x1).
- For Line 2, the slope is: (-2 - 2) / (-2 - 4) = -4 / -6 = 2 / 3
Now that we have the slopes, let's check if they are negative reciprocals of each other:
- The slope of Line 1 is -3/2.
- The slope of Line 2 is 2/3.
Since -3/2 is not the negative reciprocal of 2/3, the lines are not perpendicular to each other.
To determine if the lines are perpendicular, we can calculate the slopes of each line and check if their product is -1.
Line 1 goes through the points (-5, 0) and (-3, -3). The slope (m1) of Line 1 can be calculated using the formula:
m1 = (y2 - y1) / (x2 - x1)
Substituting the given points, we get:
m1 = (-3 - 0) / (-3 - (-5))
= (-3) / (2)
= -3/2
Line 2 goes through the points (4, 2) and (-2, -2). The slope (m2) of Line 2 can also be calculated:
m2 = (y2 - y1) / (x2 - x1)
Substituting the given points, we get:
m2 = (-2 - 2) / (-2 - 4)
= (-4) / (-6)
= 2/3
Next, we can check if the slopes of Line 1 and Line 2 multiply to give -1:
m1 * m2 = (-3/2) * (2/3)
= -1
Since the product of the slopes is -1, we can conclude that Line 1 and Line 2 are perpendicular.