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Arada [10]
2 years ago
14

The coordinates of the vertices for rectangle ABCD are A (2,4), B (6,10), C (9,8) and D (5,2). What

Mathematics
1 answer:
sweet [91]2 years ago
3 0

Answer:

D. \sqrt{65}

Step-by-step explanation:

The computation of the  length of a diagonal (AC or BD) of the rectangle is shown below:

As we know that

The Diagonal length of AC is

= (x_2 - x_1)^2 + (y_2 - y_1)^2\\\\= (9 -2)^2 + (8 - 4)^2\\\\= (7)^2 + (4)^2

= \sqrt{49 + 16}\\\\= \sqrt{65}

Therefore correct option is D.

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11 by 16

Explanation:

Set up two equations

2

x

+

2

y

=

54

x

×

y

=

176

Solving the first equation for x

2

x

+

2

y

−

2

y

=

54

−

2

y

this gives

2

x

=

54

−

2

y

Divide both sides by 2

(

2

x

2

)

=

54

−

2

y

2

This gives.

x

=

27

−

y

putting this value into the second equation gives.

(

27

−

y

)

×

y

=

176

multiplying across the parenthesis gives

27

y

−

y

2

=

176

subtracting 176 from both sides gives

is

27

y

−

y

2

−

176

=

0

multiplying by negative one gives

−

27

y

+

y

2

+

176

=

0

factoring this into y gives

(

y

−

11

)

×

(

y

−

16

)

=

0

Solving for both y's gives

y

=

11

,

y

=

16

6 0
1 year ago
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