DO NOT EXPLAIN WILL GIVE BRAINLIEST

Geometry help! Please prove the following is a square with full explanation, I'm really lost.

Hoochie [10]

We have to show that this is a square, meaning all the sides are perpendicular and the same distance.

A(3,4), B(2,-2), C(-4,-1), D(-3,5)

For each side we calculate the squared distance and the slope. We don't have to bother to take the square root. We'll subtract the points first because that difference, called the direction vector, goes into both the calculation of the slope and of the distance.

AB=B-A=(2 - 3, -2 - 4) = (-1, -6). slope=-6/-1=6 AB²=(-1)²+(-6)²=37

BC=C-B=(-6, 1). slope=1/-6=-1/6. BC²=(-6)²+1²

CD=D-C=(1, 6). slope=6/1=6 CD²=1²+6²=37

DA=A-D=(6,-1) slope=-1/6 DA²=37

We see the negative reciprocal slopes, alternating between 6 and -1/6, indicating perpendicular sides. We see they all have squared distance 37. Equal perpendicular sides proves its a square.

If we do these problems enough we learn: There's no point taking the square root. In fact, there's really no point computing the slopes and the squared distances; we can see it's a square from the pattern of the direction vectors of the sides: (-1, -6) (-6, 1) (1, 6) (6,-1)

5 0

3 years ago

Can i get the answer

Leokris [45]

Answer:

2.6

Step-by-step explanation:

by similar property

$HJ=\frac{JI\times EG}{GF}\\x+16=\frac{31\times 36}{60}\\x+16=18.6\\x=2.6$

5 0

2 years ago

Which represents the solution(s) of the graphed system of equations, y = x2 + 2x – 3 and y = x – 1?

Sonja [21]

Answer:

Second option: (-2,-3) and (1,0)

Step-by-step explanation:

Given the system of equations $\left \{ {{y = x^2 + 2x-3} \atop {y = x - 1}} \right.$ , you can rewrite them in this form:

$x^2 + 2x-3= x - 1$

Simplify:

$x^2 + 2x-3-x+1=0\\\\x^2+x-2=0$

Factor the quadratic equation. Choose two number whose sum be 1 and whose product be -2. These are: 2 and -1, then:

$(x+2)(x-1)=0\\\\x_1=-2\\\\x_2=1$

Substitute each value of "x" into any of the original equation to find the values of "y":

$y_1= (-2) - 1=-3\\\\y_2=(1)-1=0$

Then, the solutions are:

(-2,-3) and (1,0)

7 0

3 years ago

Read 2 more answers

What is the x intercepts of the mid point f(x)=(x-2)(x-4)

BigorU [14]

F(x)= -2x+6 i think so

6 0

3 years ago

Arvin has $10000 to invest. He invests part in a term deposit paying 5%/year, and the remainder in Canada savings bonds paying 3

Delicious77 [7]

Answer:

$4,562.5

Step-by-step explanation:

The amount Arvin has to invest, P = $10,000

The interest paid on the investment in the term deposit = 5%/year

The interest paid om the investment in Canada savings bonds = 3.4%/year

The amount Arvin earned at the of the year as simple interest, A = $413

Let, x, represent the amount Arvin invested in the term deposit and let, y, represent the amount he invested in Canada savings bonds, we can get the following system of equations

x + y = 10,000...(1)

0.05·x + 0.034·y = 413...(2)

Making y the subject of equation (1) and substituting the value in equation (2), we get;

From equation (1), we get, y = 10,000 - x

Plugging the above value of y in equation (2) gives;

0.05·x + 0.034 × (10,000 - x) = 413

∴ 0.05·x - 0.034·x + 340 = 413

x = (413 - 340)/(0.05 - 0.034) = 4,562.5

Therefore, the amount Arvin invested in the term deposit at 5%, x = $4,562.5

(y = 10,000 - x

∴ y = 10,000 - 4,562.5 = 5,437.5

The amount Arvin invested in Canada savings bonds, y = $5,437.5.)

8 0

2 years ago