SOLUTION: use slopes to show that the quadrilateral whose vertices are (1.-1), (4,1),(2,2), and (5,4) is a parallelogram

Question 650170: use slopes to show that the quadrilateral whose vertices are (1.-1), (4,1),(2,2), and (5,4) is a parallelogram
Found 2 solutions by sachi, MathLover1:
Answer by sachi(548) (Show Source): You can put this solution on YOUR website!
let the vertices of a quadrilateral are A(1.-1), B(4,1),C(2,2), and D(5,4)
then slope AB=[1-(-1)]/[4-1]=2/3
slope CD=[4-2]/[5-2]=2/3
so AB parallel to CD
now
slope AC=[2-(-1)]/[2-1]=3
slope BD=[4-1]/[5-4]=3
so AC parallel to BD
so ABCD is a parallelogram
ans
Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!
first, a slope for (1.-1), (4,1)

Solved by pluggable solver: Finding the slope

Slope of the line through the points (1, -1) and (4, 1)

Answer: Slope is

next, a slope for (2,2), and (5,4)

Solved by pluggable solver: Finding the slope

Slope of the line through the points (2, 2) and (5, 4)

Answer: Slope is

lines have same slope; s0, they are parallel
next, a slope for (1.-1), and (2,2)

Solved by pluggable solver: Finding the slope

Slope of the line through the points (1, -1) and (2, 2)

Answer: Slope is

and, a slope for (1.-1), and (2,2)

Solved by pluggable solver: Finding the slope

Slope of the line through the points (4, 1) and (5, 4)

Answer: Slope is

lines have same slope; s0, they are parallel
if both pairs of sides are parallel, then you can conclude that those four points define the of a

as you can see, their intersection is a

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