Can someone please help me answer this question asap thank you . No links please and thank you .

please help me, Prove a quadrilateral with vertices G(1,-1), H(5,1), I(4,3) and J(0,1) is a rectangle using the parallelogram me

mestny [16]

Answer:

Step-by-step explanation:

We are given the coordinates of a quadrilateral that is G(1,-1), H(5,1), I(4,3) and J(0,1).

Now, before proving that this quadrilateral is a rectangle, we will prove that it is a parallelogram. For this, we will prove that the mid points of the diagonals of the quadrilateral are equal, thus

Join JH and GI such that they form the diagonals of the quadrilateral.Now,

JH= $\sqrt{(5-0)^{2}+(1-1)^{2}}=5$ and

GI= $\sqrt{(4-1)^{2}+(3+1)^{2}}=5$

Now, mid point of JH= $(\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2})$

= $(\frac{5+0}{2},\frac{1+1}{2})=(\frac{5}{2},1)$

Mid point of GI= $(\frac{5}{2},1)$

Since, mid point point of JH and GI are equal, thus GHIJ is a parallelogram.

Now, to prove that it is a rectangle, it is sufficient to prove that it has a right angle by using the Pythagoras theorem.

Thus, From ΔGIJ, we have

$(GI)^{2}=(IJ)^{2}+(JG)^{2}$ (1)

Now, JI= $\sqrt{(4-0)^{2}+(3-1)^{2}}=\sqrt{20}$ and GJ= $\sqrt{(0-1)^{2}+(1+1)^{2}}=\sqrt{5}$

Substituting these values in (1), we get

$5^{2}=(\sqrt{20})^{2}+(\sqrt{5})^{2} }$

$25=20+5$

$25=25$

Thus, GIJ is a right angles triangle.

Hence, GHIJ is a rectangle.

Also, The diagonals GI= $\sqrt{(4-1)^{2}+(3+1)^{2}}=5$ and HJ= $\sqrt{(0-5)^2+(1-1)^2}=5$ are equal, thus, GHIJ is a rectangle.

6 0

3 years ago

Find the surface area, in square centimeters, of

nydimaria [60]

The surface area of the hemisphere with radius r = 19 cm. is 3400.62 square centimeters

<h3>How to determine the surface area?</h3>

The radius is given as:

r = 19

The surface area of a hemisphere is:

Area = 3πr²

So, we have:

Area = 3 * 3.14 * 19²

Evaluate

Area = 3400.62

Hence, the surface area of the hemisphere is 3400.62 square centimeters

Read more about surface areas at:

brainly.com/question/6613758

#SPJ1

8 0

2 years ago

4 to the power of 3 times 4 to the power of -1

n200080 [17]

Answer:

16 or (4^2)

Step-by-step explanation:

4^3 * 4^-1

When multiplying exponents with the same bass, the exponents themselves can be added.

3 + -1 = 2

4^2 = 16

16 is your answer!

8 0

2 years ago

Pls help i really did it plssssssssss

Bess [88]

Answer:

D

Step-by-step explanation:

You can combine like terms meaning (8x+14)+ (9x-5) is 17x+9

5 0

2 years ago

Read 2 more answers

You can do one-half of a job in you can do one half of a job in a an hour. Your friend can do one-third of the same job in an ho

AlladinOne [14]

Answer:

1.2 hours

Step-by-step explanation:

Let the amount of the job is x.

You can do 1/2x in an hour.

Your friend can do 1/3x in an hour.

<u>Together you can do:</u>

1/2x + 1/3x = 5/6x of a job in an hour

<u>You need time to finish the job:</u>

x ÷ 5/6x = 6/5 = 1.2 hours

5 0

2 years ago