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) (2 points)

Answer 1

Let's just figure out the slopes of each line to start.

Line 1 goes through (-5,0) and (-3,-3)

slope = (y2-y1)/(x2-x1) = (0- -3) / (-5 - -3) = (0+3) / (-5 + 3) = 3/-2

Line 2 goes through (4,2) and (-2, -2)

slope = (y2-y1)/(x2-x1) = (2 - -2) / (4- -2) = (2+2) / (4+2) = 4/6 = 2/3

Perpendicular lines have a negative reciprocal slope - - - - so if you can flip flop the numerator & denominator and add a negative, then it's perpendicular.

Line 1 had slope -3/2

Line 2 had slope 2/3

So yes, these are perpendicular.

Answer 2

Answer: To determine if two lines are perpendicular, we need to multiply their gradients together. If the product of their gradients is -1, then the lines are perpendicular.

Let’s first find the gradient of Line 1 that goes through (-5,0) and (-3,-3). The gradient is calculated as follows:

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

= (-3 - 0) / (-3 - (-5))

= -3/2

Now, let’s find the gradient of Line 2 that goes through (4,2) and (-2,-2). The gradient is calculated as follows:

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

= (-2 - 2) / (-2 - 4)

= -1/3

The product of the gradients is:

-3/2 * -1/3 = 1/2

Since the product of the gradients is not equal to -1, we can conclude that Line 1 and Line 2 are not perpendicular to each other.

Therefore, we can say that the lines that go through the points given below are not perpendicular.