Complete the coordinate proof of the theorem. Given: A B C D is a parallelogram. Prove: The diagonals of A B C D bisect each oth
er. Art: A parallelogram is graphed on a coordinate plane. The horizontal x-axis and vertical y-axis are solid. The vertex labeled as A lies on begin ordered pair 0 comma 0 end ordered pair. The vertex labeled as B lies on begin ordered pair a comma 0 end ordered pair. The vertex labeled as D lies on begin ordered pair c comma b end ordered pair. The vertex C is unlabeled. Diagonals A C and B D are drawn by a dotted lines. Enter your answers in the boxes. The coordinates of parallelogram ABCD are A(0, 0) , B(a, 0) , C( , ), and D(c, b) . The coordinates of the midpoint of AC¯¯¯¯¯ are ( , b2 ). The coordinates of the midpoint of BD¯¯¯¯¯ are ( a+c2 , ). The midpoints of the diagonals have the same coordinates. Therefore, AC¯¯¯¯¯ and BD¯¯¯¯¯ bisect each other.
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First box = 14 pounds
Second box = 2x = 28 pounds
Third Box = x+2= 16 pounds
Fourth box = x/2 = 7 pounds
<u>Step-by-step explanation:</u>
Here we have , Sixty-five pounds of candy was divided into four different boxes. The second box contained twice the amount of the first box. The third box contained two more pounds than the first box. The last box contained one-fourth the amount in the second box. We need to find How much candy was in each box. Let's find out:
We have a total of 65 pounds of candy ! Let in first box we have x pounds so , second box contained twice the amount of the first box i.e.
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The third box contained two more pounds than the first box i.e.
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The last box contained one-fourth the amount in the second box i.e.
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Therefore , Sum of pounds of candy are :
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Therefore , Candy in each box is :
First box = 14 pounds
Second box = 2x = 28 pounds
Third Box = x+2= 16 pounds
Fourth box = x/2 = 7 pounds