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scoundrel [369]
3 years ago
8

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

Mathematics
1 answer:
Hoochie [10]3 years ago
5 0

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)

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Answer:

0.571428571429 grams per cm³

Step-by-step explanation:

density = mass/volume

Let’s calculate the volume V of the pyramid :

V = (1/3)×base×height

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   = 105 cm³

Then

The density = mass/volume

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2 years ago
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Answer:

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e-lub [12.9K]

Answer:

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Step-by-step explanation:

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Irregular has straight lines all the way.

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Hope this helps.

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2 years ago
The height, h, in feet of a golf ball above the ground after being hit into the air is given by the equation, h = -16t 2 + 64t,
coldgirl [10]

Answer:

4 seconds

Step-by-step explanation:

When the ball is on the ground h = 0, hence

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equate each factor to zero and solve for t

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3 years ago
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nata0808 [166]

Answer:

A = 20.5 sq units

Step-by-step explanation:

you have the height of 5 but need to figure out the base

we can use the Pythagorean Theorem two times to find it

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a² = 49-25

a = \sqrt{24} = \sqrt{4}·\sqrt{6} = 2\sqrt{6}

2) b² + 5² = 6²

b² = 36-25

b = \sqrt{11}

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A = 2.5 · (2\sqrt{6} + \sqrt{11})

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A = 20.5

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3 years ago
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