Are the following lines parallel, perpindicular, or neither?
(a)x-2y=4
(b)2x+y=2
(a)-2y=-x-4
-y=-x/2-2
(b)y=-2x+2
I have that they are perpindicular. My question is this:
is -x/2 the reciprocal of 2x?
yes
Thank You
To determine if the given lines are parallel, perpendicular, or neither, we need to compare the slopes of the two lines.
For line (a): x - 2y = 4
To find the slope of this line, rearrange it into slope-intercept form (y = mx + b):
-2y = -x + 4
y = 1/2 x - 2/2
y = 1/2 x - 1
So, the slope of line (a) is 1/2.
For line (b): 2x + y = 2
Similarly, rearrange it into slope-intercept form:
y = -2x + 2
The slope of line (b) is -2.
Now, since the slopes of the two lines are negative reciprocals of each other (i.e., their product equals -1), line (a) and line (b) are perpendicular to each other.
Regarding your second question, -x/2 is indeed the reciprocal of 2x. To see this, let's find the reciprocal of 2x:
Reciprocal of 2x = 1/(2x)
To simplify the reciprocal, multiply the numerator and denominator by 1/2:
Reciprocal of 2x = (1/2)/(2x) = 1/(2 * 2x) = 1/(4x)
By comparing (-x/2) and (1/(4x)), we can see that they are reciprocals of each other. When two numbers are reciprocals, their product is always 1. Hence, -x/2 and 2x are indeed reciprocals of each other.
I hope this clarifies your doubts! Let me know if you have any more questions.