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Using Slopes of Parallel Lines Quick Check

Item 1
A quadrilateral ABCD has vertices A at (0,2), B at (2,6), C at (9,6), and D at (7,2). Are the opposite sides of this
quadrilateral parallel? (1 point)
Item 2
O Yes. AB is parallel to CD, but AD is not parallel to BC
Item 3
Item 4
O Yes. AB is parallel to CD and AD is parallel to BC
Item 5
O NO AD is parallel to BC but AB is not parallel to CD
O NO AB is parallel to CD, and AD is parallel to BC

User Asim Roy
by
7.9k points

1 Answer

3 votes

Answer:

The answer is (B)Yes. AB is parallel to CD and AD is parallel to BC

Explanation:

There is an important fact about the parallel lines:

  • Parallel lines have equal slopes

The rule of the slope of a line is:


  • m=(y_(2)-y_(1) )/(x_(2)-x_(1)), where
    (x_(1),y_(1)) and
    (x_(2),y_(2)) are two points on the line

Let us use the fact and the rule to solve the question

∵ ABCD is a quadrilateral

∵ A = (0, 2) , B = (2, 6), C = (9, 6), D = (7, 2)

∵ The opposite sides are AB, CD and AD, BC

Find the slopes of the four sides to check the parallel sides


m_(AB)=(6-2)/(2-0)=(4)/(2)=2


m_(CD)=(2-6)/(7-9)=(-4)/(-2)=2

∵ The slope of AB = The slope of CD

AB // CD


m_(AD)=(2-2)/(7-0)=(0)/(7)=0


m_(BC)=(6-6)/(9-2)=(0)/(7)=0

∵ The slope of AB = The slope of CD

AD // BC

The correct answer is:

Yes. AB is parallel to CD and AD is parallel to BC ⇒ (B)

User NFG
by
8.4k points

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