Answer:
The equation of the line parallel to y=4/3x−4 that passes through (-4,6) is y=4/3x−10/3 .
The equation of the line perpendicular to y=43x−4 that passes through (-4,6) is y=−3/4x+10 .
Step-by-step explanation:
Parallel means equal slopes. Hence, the slope of the line parallel to y=4/3x+3 is 4/3 . We know our slope and we know a point. We can therefore use point-slope form to determine the equation of the new line.
y−y1=m(x−x1)
y−6=4/3(x−4)
y−6=4/3x−16/3
y=4/3x−7/3
The equation of the line parallel to y=4/3x−4 that passes through (-4,6) is y=4/3x−10/3 .
Question #2:
Perpendicular means negative reciprocal slopes. Hence, the slope perpendicular to y=4/3x+3 is y=−3/4 . We know our slope and we know a point. We can therefore use point-slope form to determine the equation of the new line.
y−y1=m(x−x1)
y−6=−3/4(x-4)
y−6=−3/4x+6
y=−3/4x+10
The equation of the line perpendicular to y=43x−4 that passes through (-4,6) is y=−3/4x+10 .
8. The corresponding angles of similar triangles are congruent. Angle U corresponds to angle R, so the value of x will be the value of the unmarked angle in ∆PRQ. The sum of angles is 180°, so the unmarked angle (x) has measure ...
... x = 180° - 60° - 40° = 80° . . . . matches selection A
9. The ratio of the lengths of the original to its image is the same in all cases. The appropriate choice is ...
... B. AB/A'B' = BC/B'C'
The other choices have mixed ratios that don't make any sense.
10. The parallel base makes ∆RTU ~ ∆RQS and divides RQ in the same proportion it divides RS. The appropriate choice here is ...
... C. RT/TQ = RU/US
