What to the power of 2 equals 9/16

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 greatest three digit number divisible by 12,18,24.

Karolina [17]

Your answer is 6.

6*2=12

6*3=18

6*4=24

5 0

3 years ago

TV=3x-24 and VX=2x+1. What is the value of VX? 1. 25 2. 99 3. 5 4. 51

Maslowich

ΔTXV is an isosceles triangle because ∡T = ∡X therefore TV = VX.

3x - 24 = 2x + 1 |subtract 2x from both sides

x - 24 = 1 |add 24 to both sides

x = 25

7 0

3 years ago

Read 2 more answers

666.6 to nearest integer

kari74 [83]

Answer:Redondeo al entero más cercano, ejemplos. Denotemos por ρ a la función de un argumento real que lo redondea un número real más cercano: ρ(7.394) = 8,.

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers

Tim is running extremely late and has just 5 minutes to return his rental car to the agency. The fuel tank in the car is half em

Whitepunk [10]

Answer:

B

Step-by-step explanation:

Although this problem is quite long and exhausting, it is deceptively simple.

We know that his 12-gallon fuel tank is only half full, so we know that the car needs 6 more gallons of fuel.

If he turns in the car late, he will have to pay y = 2.59x + 32.00, where x is the number of empty gallons (in this case, 6)

In this case, he will pay 2.59(6) + 32.00 = $47.54

If he turns in the car on time, he will have to pay y = 4.50x + 5.00, where x is the number of empty gallons (still 6).

In this case, he will pay 4.50(6) + 5.00 = $32.00

Using these results, we know that B must be true.

4 0

3 years ago