Question 266118
we need the distance formula as
{{{d = sqrt((y2-y1)^2 + (x2-x1)^2)}}}
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distance between: (-1,-1), (9,4) is
{{{d = sqrt((4-(-1))^2 + (9-(-1))^2)}}}
or
{{{d = sqrt((5)^2 + (10)^2)}}}
and then
{{{d = sqrt(125)}}}
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distance between: (9,4), (20,6) is
{{{d = sqrt((6-(4))^2 + (9-(20))^2)}}}
or
{{{d = sqrt((2)^2 + (-11)^2)}}}
and then
{{{d = sqrt(125)}}}
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distance between: (20,6), and (10,1) is
{{{d = sqrt((1-(6))^2 + (10-(20))^2)}}}
or
{{{d = sqrt((-5)^2 + (-10)^2)}}}
and then
{{{d = sqrt(125)}}}
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distance between: (-1,-1), and (10,1) is
{{{d = sqrt((1-(-1))^2 + (10-(-1))^2)}}}
or
{{{d = sqrt((2)^2 + (-11)^2)}}}
and then
{{{d = sqrt(125)}}}
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So we have shown we have a square with all sides equal. SInce the angles are all not 90 degrees, we have a rhombus.
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area = diagonal 1 x diagonal 2 / 2
diagonal 1 = sqrt(21^2 + 7^2) = sqrt(490)
diagonal 2 = sqrt(1^2 + 3^2) = sqrt(10)
area = sqrt(490) * sqrt(10)/2 = 35