Mathematics, 02.08.2019 20:30 zahraalshagawa02

Determine whether a figure with the given vertices is a rectangle using the distance formula.
a(4, –7), b(4, –2), c(0, –2), d(0, –7)
question 14 options:
yes; opposite sides are congruent.
yes; opposite sides are congruent, and diagonals are congruent.
yes; opposite sides are parallel.
no; opposite sides are congruent, but diagonals are not congruent.

Answers: 3

Show answers

Answers

Answer from: angelhusted213

Yes; Opposite sides are congruent, and diagonals are congruent.

Step-by-step explanation:

we have

A(4, -7), B(4, -2), C(0, -2), D(0, -7)

we know that

the formula to calculate the distance between two points is equal to

$d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}$

step 1

Find the length of the sides

Find the distance AB

substitute the values

$d=\sqrt{(-2+7)^{2}+(4-4)^{2}}$

$d=\sqrt{(5)^{2}+(0)^{2}}$

$AB=5\ units$

Find the distance BC

substitute the values

$d=\sqrt{(-2+2)^{2}+(0-4)^{2}}$

$d=\sqrt{(0)^{2}+(-4)^{2}}$

$BC=4\ units$

Find the distance CD

substitute the values

$d=\sqrt{(-7+2)^{2}+(0-0)^{2}}$

$d=\sqrt{(-5)^{2}+(0)^{2}}$

$CD=5\ units$

Find the distance AD

substitute the values

$d=\sqrt{(-7+7)^{2}+(0-4)^{2}}$

$d=\sqrt{(0)^{2}+(-4)^{2}}$

$AD=4\ units$

Compare the length sides

AB=CD

BC=AD

therefore

Opposite sides are congruent

step 2

Find the length of the diagonals

Find the distance AC

substitute the values

$d=\sqrt{(-2+7)^{2}+(0-4)^{2}}$

$d=\sqrt{(5)^{2}+(-4)^{2}}$

$AC=\sqrt{41}\ units$

Find the distance BD

substitute the values

$d=\sqrt{(-7+2)^{2}+(0-4)^{2}}$

$d=\sqrt{(-5)^{2}+(-4)^{2}}$

$BD=\sqrt{41}\ units$

Compare the length of the diagonals

AC=BD

therefore

Diagonals are congruent

The figure is a rectangle, because Opposite sides are congruent, and diagonals are congruent

Answer from: maisieisdabomb23

The correct option is 2.

Step-by-step explanation:

Given information: A(4, –7), B(4, –2), C(0, –2), D(0, –7).

Distance formula:

$D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Using distance formula we get

Length of sides are

$AB=\sqrt{\left(4-4\right)^2+\left(-2-\left(-7\right)\right)^2}$

$AB=\sqrt{(0)^2+(-2+7)^2}$

$AB=\sqrt{5^2}=5$

Similarly,

$BC=\sqrt{\left(0-4\right)^2+\left(-2-\left(-2\right)\right)^2}=4$

$CD=\sqrt{\left(0-0\right)^2+\left(-7-\left(-2\right)\right)^2}=5$

$AD=\sqrt{\left(0-4\right)^2+\left(-7-\left(-7\right)\right)^2}=4$

Length of diagonals are

$AC=\sqrt{\left(0-4\right)^2+\left(-2-\left(-7\right)\right)^2}=\sqrt{41}$

$BD=\sqrt{\left(0-4\right)^2+\left(-7-\left(-2\right)\right)^2}=\sqrt{41}$

It figure ABCD,

1. AB and CD are opposite sides.

2. BC and AD are opposite sides.

3. AC and BD are diagonals.

From the above calculations it is clear that opposite sides are congruent, and diagonals are congruent. So, the figure ABCD is a rectangle.

Therefore the correct option is 2.

Answer from: Quest

a negative exponent is translated as follows:

$a^{-m} = \dfrac{1}{a^m}$

so, we have

$\left(5^{-1}+3^{-1}+2^{-1}\right)^{-1} = \left(\dfrac{1}{5}+\dfrac{1}{3}+\dfrac{1}{2}\right)^{-1} = \left(\dfrac{6+10+15}{30}\right)^{-1}=\left(\dfrac{31}{30}\right)^{-1}=\dfrac{30}{31}$

Answer from: Quest

first anwser choice.

step-by-step explanation:

the greater/less or equal to symbol (> or < with the line at the bottom) is a closed/filled in circle.

when multiplying or dividing by a negative on both sides you have to flip the inequality sign. this rule only applies to multiplying or dividing by a negative number in inequality equations. this rule is really important.

-5c + 2 _< _27

subtract from both sides by 2

-5c _< _ 27

divide both sides by -5

c _< _ 5.4

flip the inequality sign

c _> _5.4

the only possible answer that would match the simplified inequality is the first answer choice

5c+2< 27 i really do not understand this.

Another question on Mathematics

Mathematics, 21.06.2019 18:00

If the cost to mail a package is an initial $5 and $0.28 for every pound the total cost to mail a package was $11.27, how much did the package weigh?

Answers: 1

Answer

Mathematics, 21.06.2019 20:50

In the diagram, gef and hef are congruent. what is the value of x

Answers: 1

Answer

Mathematics, 21.06.2019 23:10

Which best describes the function on the graph? direct variation; k = −2 direct variation; k = -1/2 inverse variation; k = −2 inverse variation; k = -1/2

Answers: 2

Answer

Mathematics, 22.06.2019 02:30

Polynomials plz quick 1: subtract and simplify (–y^2 – 4y – 8) – (–4y^2 – 6y + 3)

Answers: 1

Answer

You know the right answer?

Determine whether a figure with the given vertices is a rectangle using the distance formula.
...

Questions