Geometry Cumilitive Review

Question

4.Given a line through (-3,4) and (4,-3) and a line through (-6,-5) and (-5,-4). Determine if these lines are parallel,perpendicular or niether. Show all work

5.A line through point (-6,4) is perpindicular to the line y=1/2x+2.Find the euation of the line through point (-6,4).

Answer 1

4) slope is change in y over change in x

slope 1 = (-3 - 4)/(4 - (-3)) = -7/7 = -1

slope 2 = (-4 - (-5))/(-5 - (-6)) = 1/1 = 1

perpendicular lines have negative reciprocal slopes, so these lines are perpendicular

5) the slope of the line y = 1/2 x + 2 is 1/2, so the slope of the perpendicular line is -2

y = mx + b, plug in (-6, 4) and slope = -2

4 = -2(-6) + b

4 = 12 + b

-8 = b

so y = -2x -8