Question

BRAINLIEST PLUS POINTS

Answer 1

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

$\frac{y_2-y_1}{x_2-x_1}$

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

Answer 2

Answer:

a) (0,2)

b) 1

c) -1×1 = -1

d) ½(AC)(EB)

Step-by-step explanation:

a) e = (-1+1)/2, (3+1)/2 = 0,2

e = (0,2)

b) Slope = (2-4)/(0-2) = -2/-2 = 1

c) slope of AC = (3-1)/(-1-1) = 2/-2 = -1

Slope AC × Slope EB = -1 × 1 = -1

So, Perpendicular

d) since AC and EB are Perpendicular, they can be considered as base and height of the triangle

Area = ½(AC)(EB)