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emmainna [20.7K]
3 years ago
8

A (1, -3) B (1, 0) C (4, 2) Parallelogram ABCD has the coordinates: Find the coordinates of point D.

Mathematics
1 answer:
EleoNora [17]3 years ago
3 0

Answer:

(4,-1)

Step-by-step explanation:

Given

3 Co-ordinates of a parallelogram ABCD

A=(1,-3)

B=(1,0)

C=(4,2)

D=(a,b)

One of the property of a parallelogram is that the diagonals bisect each other

In this case, AC and BD bisect each other, Therefore the middle point of AC and BD coincide

⇒Mid-point of AC= Mid-point of BD

(mid point of 2 points (x,y) and (k,l) is =(\frac{(k+x)}{2} ,\frac{(l+y)}{2}))

(\frac{(1+4)}{2} ,\frac{(-3+2)}{2})=(\frac{(1+a)}{2} ,\frac{(0+b)}{2})\\(\frac{5}{2} ,\frac{-1}{2})=(\frac{(1+a)}{2} ,\frac{b}{2})

Compare x and y co-ordinates on both sides

⇒\frac{5}{2} =\frac{1+a}{2}

a=4

⇒\frac{-1}{2}=\frac{b}{2} }

b=-1

Therefore D=(4,-1)

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Reason 2. AB is parallel to DC - given

Reason 3. angle BAC is congruent to angle DCA - alternate interior angles are congruent

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When the numbers are relatively close together, it is often useful to see if their difference is a factor:

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<em>How to find the greatest common factor (GCF)</em>

The Euclidean algorithm has you find the remainder from division of the larger by the smaller. If that remainder is zero, the smaller is the GCF. If the remainder is nonzero, it replaces the larger number and the process is repeated. When the larger number is less than twice the smaller, the remainder is their difference.

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