Which of the following show the Associative Property?

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

(NEED HELP! WILL RATE 5 STARS!)

vitfil [10]

Answer:I think it's 1/61

Step-by-step explanation:If I am correct plz don't forget to thank me...

3 0

2 years ago

The economics department has 40 applicants for their phd program and only 10 openings. how many different combinations of applic

lana66690 [7]

In a sequence of events, the total possible number of ways all events can performed is the product of the possible number of ways each individual event can be performed. Since there are 10 openings

<span>P = 40 x 39 x 38 x 37 x 36 x 35 x 34 x 33 x 32 x 31 = 3.07599 x 10^15 different combinations</span>

5 0

3 years ago

Pweaseee help!!!!!!!!!!!!!

juin [17]

Answer:

Andre.

Step-by-step explanation:

Andre's group was asked to write an expression equivalent to 5p²q + 7pq² - 10.

Andre gives the expression 7p²q + 7pq² - 1 - 2p²q - 9, which gives the expression 5p²q + 7pq² - 10.

Jill gives the expression 5p²q + 2 pq² - 6 + 5pq² - 3, which does not give the expression 5p²q + 7pq² - 10.

Now, Anuj gives the expression 4p²q + 7pq²- 7 + 2p²q - 3, which also does not give the expression 5p²q + 7pq² - 10.

Again, Marsha gives the expression 5p²q + 5 pq²- 10 + 3pq², which also does not gives the expression 5p²q + 7pq² - 10.

Hence, only Andre gives the correct expression. (Answer)

5 0

3 years ago

Find the y intercept of the line on the graph

melisa1 [442]

Answer:

(0, -4)

Step-by-step explanation:

because the y is the vertical line. (the one that is going up and down)

and it intercepts the blue line at (0, -4)

3 0

2 years ago