Answered

Given that the points (-5, 7), (5, 7), (5, 1), and (-5, 1) are vertices of a rectangle, how much shorter is the width than the length?

A-5 units
B-4 units
C-3 units
D-2 units

Any improper answers will be reported.

Thanks you.

Verified Answer :

hbarisk

(-5,7) and (-5,1) is the left side of the rectangle and the width is 7-1 =6
(5,7) and (5,1) is the right side of it. And length will be 5+5 = 10

And difference is 4.

Answer:  The correct option is (B) - 4 units.

Step-by-step explanation:  Given that the points  (-5, 7), (5, 7), (5, 1), and (-5, 1) are vertices of a rectangle.

We are to find the shortness of the width as compared to the length.

Since the adjacent sides of a rectangle makes the length and breadth of the rectangle, so the lengths of two adjacent sides are calculate using distance formula as follows:

the length of the line segment joining the points (-5, 7) and (5, 7) is

\(l_1=\sqrt{(-5-5)^2+(7-7)^2}=\sqrt{100+0}=\sqrt{100}=10~\textup{units},\)

and the length of the line segment joining the points (5, 7) and (5, 1) is

\(l_2=\sqrt{(5-5)^2+(7-1)^2}=\sqrt{0+36}=\sqrt{36}=6~\textup{units},\)

So, the length of the rectangle is 6 units and breadth of the rectangle is 10 units.

Therefore, the width is shorter than the length by

\(l_2-l_1=6-10=-4~\textup{units}.\)

Thus, (B) is the correct option.

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