1.) Given points A(-4, 5), B(2, 3), C(0, 4) and D(5, 0), decide if AB and CD are parallel, perpendicular or neither.
2.)Given the equations y = 1x + 7 and y = 3x - 2, decide whether the lines are parallel, perpendicular or neither.
3.) Given the equations y = 4/3x - 3 and y = -3/4x + 2, decide whether the lines are parallel, perpendicular, or neither.
If two lines are parallel then their slopes are equal
If two lines are perpendicular, their slopes are negative reciprocals of each other (opposite in sign and the fraction is flipped)
for the first one, find
slope(AB) and slope(CD), and decide
second is very easy
slope of first is 1
slope of second is 3
"nothing to see here, folks"
the third:
slope of first is 4/3
slope of second is -3/4
mmmhhh?
Thanks :)
6+7
To determine whether two lines are parallel, perpendicular, or neither, we need to find their slopes. The slope of a line is given by the formula (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are two points on the line.
Let's solve the first question:
1.) Given points A(-4, 5), B(2, 3), C(0, 4), and D(5, 0), we need to find the slopes of the lines AB and CD.
The slope of line AB is (y2 - y1) / (x2 - x1), which can be calculated as (3 - 5) / (2 - (-4)) = -2 / 6 = -1/3.
The slope of line CD is (y2 - y1) / (x2 - x1), which can be calculated as (0 - 4) / (5 - 0) = -4 / 5 = -4/5.
Since the slopes of AB (-1/3) and CD (-4/5) are different, the lines are not parallel. Furthermore, the product of the slopes (-1/3 * -4/5) is not equal to -1, so the lines are also not perpendicular. Therefore, AB and CD are neither parallel nor perpendicular.
Now let's solve the second question:
2.) Given the equations y = 1x + 7 and y = 3x - 2, we can see that the coefficients of x in the two equations (1 and 3) are not the same. Therefore, the lines are not parallel.
To determine whether the lines are perpendicular, we need to compare the slopes. The slope of the first line is 1, and the slope of the second line is 3. Since the product of the slopes (1 * 3) is not equal to -1, the lines are not perpendicular either. Therefore, the lines y = 1x + 7 and y = 3x - 2 are neither parallel nor perpendicular.
Finally, let's solve the third question:
3.) Given the equations y = 4/3x - 3 and y = -3/4x + 2, we can see that the coefficients of x in the two equations (4/3 and -3/4) are not the same. Therefore, the lines are not parallel.
To determine whether the lines are perpendicular, we need to compare the slopes. The slope of the first line is 4/3, and the slope of the second line is -3/4. Since the product of the slopes ((4/3) * (-3/4)) is equal to -1, the lines are perpendicular.
Therefore, the lines y = 4/3x - 3 and y = -3/4x + 2 are perpendicular to each other.