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)

Question

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)

Answer 1

To determine if the lines are perpendicular, we need to find the slopes of Line 1 and Line 2 by using the formula:

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

For Line 1:
slope of Line 1 = (-3 - 0) / (-3 - (-5)) = -3 / 2 = -1.5

For Line 2:
slope of Line 2 = (-2 - 2) / (-2 - 4) = -4 / -6 = 2/3

If the product of the slopes of two lines is -1, then the lines are perpendicular.

In this case, (-1.5) * (2/3) = -1, so Line 1 and Line 2 are perpendicular.

Answer 2

To determine if two lines are perpendicular, we need to check if the slopes of the lines are negative reciprocals of each other.

Let's start by finding the slopes of the given lines.

For Line 1, which goes through points (-5,0) and (-3,-3):
The slope of Line 1 (m1) can be found using the formula:
m1 = (y2 - y1) / (x2 - x1)
m1 = (-3 - 0) / (-3 - (-5))
m1 = -3 / (-3 + 5)
m1 = -3 / 2

For Line 2, which goes through points (4,2) and (-2,-2):
The slope of Line 2 (m2) can be found using the same formula:
m2 = (y2 - y1) / (x2 - x1)
m2 = (-2 - 2) / (-2 - 4)
m2 = -4 / (-2 - 4)
m2 = -4 / (-6)
m2 = 2 / 3

Now, let's check if the slopes are negative reciprocals of each other:
The negative reciprocal of -3/2 is -2/3, which is the slope of Line 2 (m2).
Therefore, the two lines are indeed perpendicular to each other.

In conclusion, the lines Line 1 and Line 2 are perpendicular because their slopes are negative reciprocals of each other.

Answer 3

To determine if two lines are perpendicular, we need to check the slopes of the lines. If the product of the slopes is -1, then the lines are perpendicular.

Let's calculate the slopes of Line 1 and Line 2:

For Line 1:
We have two points: (-5,0) and (-3,-3).
The slope of a line passing through two points (x₁, y₁) and (x₂, y₂) is given by the formula:
slope = (y₂ - y₁) / (x₂ - x₁)

Using the points we have, the slope of Line 1 is:
slope 1 = (-3 - 0) / (-3 - (-5))
= -3 / 2
= -1.5

For Line 2:
We have two points: (4,2) and (-2, -2).
Using the same formula, the slope of Line 2 is:
slope 2 = (-2 - 2) / (-2 - 4)
= -4 / -6
= 2/3

Now, let's check if these slopes are perpendicular.
The product of the slopes is -1:
slope 1 * slope 2 = (-1.5) * (2/3) = -1

Since the product of the slopes is -1, we can conclude that Line 1 and Line 2 are perpendicular.