If two opposite sides of a quadrilateral are perpendicular and congruent, then the quadrilateral is a parallelogram.
1 answer:
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Answer:
d(x) = √[(x - 2)² + (3x - 1)²]
Step-by-step explanation:
The distance between two points with coordinates (x₁, y₁) and (x₂, y₂) is given as
d = √[(x₂ - x₁)² + (y₂ - y₁)²]
So, the distance between point (2,0) and a point (x,y)
d = √[(x - 2)² + (y - 0)²]
d = √[(x - 2)² + (y)²]
But the point (x,y) is on the line y = 3x - 1
We can substitute for y in the distance between points equation.
d(x) = √[(x - 2)² + (3x - 1)²]
QED!
First, we need to equalize the denominator. If the denominator multiplies by (x+1), so does the numerator. If the denominator multiplies by (x-1), so does the numerator.
Look into my attachment at the second row.
Second, because the first fraction and the second fraction have the same denominator, you can join them into one fraction.
Look into my attachment at the third row.
Third, simplify the numerator.
Look into my attachment at the fourth to the fifth row
Fourth, simplify the denominator.
Look into my attachment at the sixth to the seventh row.
Look into my attachment at the second row.
Second, because the first fraction and the second fraction have the same denominator, you can join them into one fraction.
Look into my attachment at the third row.
Third, simplify the numerator.
Look into my attachment at the fourth to the fifth row
Fourth, simplify the denominator.
Look into my attachment at the sixth to the seventh row.