Answer:
a) e(0,2)
b) 1
c) read below
d) read below
Step-by-step explanation:
Midpoint:
to calculate the midpoint e of a segment
e((x1+x2)/2, (y1+y2)/2)
so (-1+1)/2 and (3+1)/2
e(0,2)
Slope formula:
the slope of a straight line between two points is
so between e and B it's equal to (4-2)/(2-0) = 1
Condition for perpendicularity : slope(AC) = -1/slope(eB) = -1
so we calculate the slope of a straight line through A and C
(1-3)/1-(-1) = -2/2 = -1 so they are perpendicular
Area:
eB is the height of the triangle as it's perpendicular to the base, so applying the standard formula Area = (AC*eB)/2 we can find the area