They have M(2,4) and N(1,2). Find the equation of the line and the equation that creates a 90° angle with the line through 0.

Question

1st question is to find the line equation.

2nd is to find the line that create a 90° when meeting it and also the new line needs to be through (0,0).

Answer 1

THe given line, call it L, passes through (2,4) and (1,2).

We want a line that is PERPENDICULAR to L and passes through the origin (0,0)

The slope of the given line is m=(4-2)/(2-1) = 2/1 = 2

Perpendicular lines have slopes that are NEGATIVE RECIPROCALS.

So, the slope of the perpendicular line is (-1/2)

Since the perpendicular line passes through (0,0) we have

x=0, y=0 and slope m=(-1/2)

THe intercept of any line is B = y - mx = 0 - (-1/2)(0) = 0

So the equation of the perpendicular line is y = (-1/2)x + 0 = (-1/2)x

Therefore, if you graph the line through (2,4) and (1,2) vs y = (-1/2)x

they will be perpendicular (meet at 90 right angles) and the latter

will eat (0,0)