Which pair of slopes could represent perpendicular lines
1/7 ,7
1/2 , 2/4
-3/4, 4/3
1/3, 1/3
The pair of slopes that could represent perpendicular lines is 1/7 and -7.
To determine which pair of slopes could represent perpendicular lines, we need to check if the product of the slopes is equal to -1.
Let's calculate the products of each pair of slopes:
1/7 * 7 = 7/7 = 1
1/2 * 2/4 = 2/8 = 1/4
-3/4 * 4/3 = -12/12 = -1
1/3 * 1/3 = 1/9
From the calculations above, we can see that the pair of slopes -3/4 and 4/3 gives us a product of -1. Therefore, the pair of slopes -3/4, 4/3 could represent perpendicular lines.
To determine which pair of slopes represents perpendicular lines, we need to use the property that the slopes of perpendicular lines are negative reciprocals of each other.
The negative reciprocal of a slope is obtained by flipping the fraction and changing the sign (positive to negative or negative to positive).
Let's calculate the negative reciprocals for each pair of slopes:
1/7: The negative reciprocal is -7/1=-7.
1/2: The negative reciprocal is -2/1=-2.
-3/4: The negative reciprocal is 4/3.
1/3: The negative reciprocal is -3/1=-3.
Now, let's examine the pair of slopes:
1/7 and 7: The slopes are not negative reciprocals of each other.
1/2 and 2/4: The slopes are not negative reciprocals of each other.
-3/4 and 4/3: The slopes are negative reciprocals of each other.
1/3 and 1/3: The slopes are not negative reciprocals of each other.
Therefore, the pair of slopes -3/4 and 4/3 represents perpendicular lines because their slopes are negative reciprocals of each other.