Question

I need help with Geometry

Answer 1

The correct answer is:

Option 2: Yes, because the slopes of lines are negative reciprocals.

Explanation:

Given equations of lines are:

Line p: x+2y=1

Line q: y=2x+1

We can determine if two lines are parallel or perpendicular by comparing the slopes of line.

Slope intercept form of line is given by the formula

`y = mx+b`

Equation of line q is already in slope intercept form.

We have to convert the equation of line p in slope-intercept form

`x+2y = 1\\2y = -x+1\\2y = -(1)/(2)x+(1)/(2)`

Slope of line p = 2

Slope of line q = -1/2

We can see that

`2.-(1)/(2) = -1`

The product of slopes of both lines is -1, hence, the lines are perpendicular.

Hence,

The correct answer is:

Option 2: Yes, because the slopes of lines are negative reciprocals.