What is the area of triangle GHJ

Mathematics

1 answer:

EastWind [94]4 years ago

4 0

A = 1/2 bh = 1/2 (3)(4) = 12/2 = 6

answer is B. 6 square units

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if A(-2,1), B(1,5), C(4,4), D(1,0) are the vertices of a quadrilateral, do the points form a parallelogram? Justify your answer.

4vir4ik [10]

We have that

<span>A(-2,1), B(1,5), C(4,4), D(1,0)
</span>using a graph tool
see the attached figure

we know that
A parallelogram is a simple quadrilateral with opposite sides parallel and equal in length
therefore
<span>let's calculate the slope and distance of each side and compare them
</span>
side AB
slope m=(y2-y1)/(x2-x1)------> m=(5-1)/(1+2)----> m=4/3
distance AB=√4²+3³-------> dAB=5 units

side CD
slope m=(y2-y1)/(x2-x1)------> m=(0-4)/(1-4)----> m=4/3
distance CD=√4²+3³-------> dCD=5 units

side BC
slope m=(y2-y1)/(x2-x1)------> m=(4-5)/(4-1)----> m=-1/3
distance BC=√1²+3³-------> dBC=√10 units

side AD
slope m=(y2-y1)/(x2-x1)------> m=(0-1)/(1+2)----> m=-1/3
distance AD=√1²+3³-------> dAD=√10 units

(side BC and side AD are parallel) and (side BC=side AD)
and
(side AB and side CD are parallel) and (side AB=side CD)

therefore

the answer is
Yes, it is a parallelogram