is the line through points P(-8,10)and Q(-5,-12) perpendicular to the line through points R(9,-6) and S(17,-5)? Explain
PQ has slope (12-10)/(-5+8) = 2/3
RS has slope (-5+6)/(17-9) = 1/8
so the lines are not ⊥
why not?
Well, let's find out if these two lines are perpendicular! To do that, we need to check if the slopes of these lines are negative reciprocals of each other.
First, let's find the slope of the line passing through points P(-8,10) and Q(-5,-12). The formula for slope (m) is:
m = (y2 - y1) / (x2 - x1)
So, the slope of line PQ is:
m1 = (-12 - 10) / (-5 - (-8))
= (-22) / (3)
Now let's find the slope of the line passing through points R(9,-6) and S(17,-5). Similar to before:
m = (y2 - y1) / (x2 - x1)
So, the slope of line RS is:
m2 = (-5 - (-6)) / (17 - 9)
= (1) / (8)
Now, if the lines are perpendicular, then the product of their slopes should be -1. Let's check that:
m1 * m2 = ((-22) / 3) * (1 / 8)
= (-22/24)
= -11/12
Hmm, it looks like the product of the slopes is not -1. So, these two lines are not perpendicular to each other.
Now, as a clown bot, I can't resist adding a joke here.
Why don't scientists trust atoms?
Because they make up everything!
But I know that wasn't what you were looking for, so I hope the explanation was helpful!
To determine if the line through points P(-8,10) and Q(-5,-12) is perpendicular to the line through points R(9,-6) and S(17,-5), we can compare the slopes of the two lines.
The slope of a line can be found using the formula:
m = (y2 - y1) / (x2 - x1),
where (x1, y1) and (x2, y2) are the coordinates of two points on the line.
For the line through points P(-8,10) and Q(-5,-12), the slope can be calculated as:
m1 = (-12 - 10) / (-5 - (-8))
= (-22) / (3)
= -22/3.
For the line through points R(9,-6) and S(17,-5), the slope can be calculated as:
m2 = (-5 - (-6)) / (17 - 9)
= (1) / (8)
= 1/8.
If two lines are perpendicular, their slopes are negative reciprocals of each other. In other words, the product of their slopes should be equal to -1.
Let's check if the slopes we calculated satisfy this condition:
m1 * m2 = (-22/3) * (1/8)
= -22/24
= -11/12.
Since m1 * m2 is not equal to -1, the line through points P(-8,10) and Q(-5,-12) is not perpendicular to the line through points R(9,-6) and S(17,-5).
Therefore, these two lines are not perpendicular to each other.
To determine if two lines are perpendicular, we can check if the product of their slopes is -1.
First, let's find the slope of the line passing through points P(-8,10) and Q(-5,-12):
Slope (m) = (change in y) / (change in x)
m = (-12 - 10) / (-5 - (-8))
m = (-22) / (3) = -22/3
Next, let's find the slope of the line passing through points R(9,-6) and S(17,-5):
Slope (m) = (change in y) / (change in x)
m = (-5 - (-6)) / (17 - 9)
m = (1) / (8) = 1/8
Now, let's check if the product of the slopes is -1:
(-22/3) * (1/8) = -22/24 = -11/12 ≠ -1
Since the product of the slopes is not equal to -1, the line passing through points P(-8,10) and Q(-5,-12) is not perpendicular to the line passing through points R(9,-6) and S(17,-5).
Therefore, the answer is no, the lines are not perpendicular.