Use the slopes to determine if the line between the points (3, 5) and (-2, 7) is parallel, perpendicular or neither to a line that passes through the points (10,5) and (6, 15)
a) Parallel
b) Perpendicular
c) Neither
so, can you not figure the slopes?
The first has slope (7-5)/(-2-3) = -2/5
you do the other, and then recall that
parallel lines have equal slopes
perpendicular lines have slopes whose product is -1
To determine if two lines are parallel or perpendicular, we need to compare their slopes. We can do this using the slope-intercept form of a linear equation: y = mx + b, where m is the slope.
Step 1: Find the slope of the first line.
The slope between the points (3, 5) and (-2, 7) can be found using the formula:
m1 = (y2 - y1) / (x2 - x1)
Substituting the coordinates (3, 5) and (-2, 7):
m1 = (7 - 5) / (-2 - 3)
= 2 / (-5)
= -2/5
So, the slope of the first line is -2/5.
Step 2: Find the slope of the second line.
Similarly, we can find the slope between the points (10, 5) and (6, 15):
m2 = (15 - 5) / (6 - 10)
= 10 / (-4)
= -5/2
So, the slope of the second line is -5/2.
Step 3: Compare the slopes.
If the slopes are equal, the lines are parallel. If the slopes are negative reciprocals of each other (i.e., their product equals -1), the lines are perpendicular. Otherwise, the lines are neither parallel nor perpendicular.
To determine this, we'll calculate the product of the slopes:
m1 * m2 = (-2/5) * (-5/2)
= 1
Since the product of the slopes is 1, which is not -1, the lines are neither parallel nor perpendicular. Therefore, the answer is:
c) Neither