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2 years ago

What kind of quadrilateral is PQRS? EXPLAIN YOUR REASONING.

Mathematics

1 answer:

aleksandr82 [10.1K]2 years ago

6 0

Answer:

PS = 3
SR = 3
PQ = √29
QR = √29
kite

Step-by-step explanation:

A quadrilateral with perpendicular diagonals, one of which is a line of symmetry, is a <em>kite</em>.

Perhaps a more conventional definition of a kite is that it is a quadrilateral with two pairs of congruent adjacent sides.

The lengths PS and SR can be found by counting grid squares along the line segments. Each has a length of 3. They constitute one pair of congruent adjacent sides.

PS = SR = 3

The lengths of PQ an QR can be found using the distance formula. Essentially, it uses the Pythagorean theorem to compute the hypotenuse of a right triangle whose legs are the differences in x- and y-coordinates. For PQ and QR, those differences are 2 and 5, so the lengths of those segments are √(2² +5²) = √29.

PQ = QR = √29

The figure has two pairs of congruent adjacent sides, so is a <em>kite</em>.

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3 years ago

Read 2 more answers

NEED HELP Find values for a, b, c, and d so that the following matrix product equals the 2X2 identity matrix. Explain or show ho

ehidna [41]

We want to find the values of a, b, c, and d such that the given matrix product is equal to a 2x2 identity matrix. We will solve a system of equations to find:

b = 1
a = -1
c = -2
d = -1

<h3>Presenting the equation:</h3>

Basically, we want to solve:

$\left[\begin{array}{cc}-1&2\\a&1\end{array}\right]*\left[\begin{array}{cc}b&c\\1&d\end{array}\right] = \left[\begin{array}{cc}1&0\\0&1\end{array}\right]$

The matrix product will be:

$\left[\begin{array}{cc}-b + 2&-c + 2d\\a*b + 1&a*c + d\end{array}\right]$

Then we must have:

-b + 2 = 1

This means that:

b = 2 - 1 = 1

b = 1

We also need to have:

a*b + 1 = 0

we know the value of b, so we just have:

a*1 + b = 0

a = -1

Now the two remaining equations are:

-c + 2d = 0

a*c + d = 1

Replacing the value of a we get:

-c + 2d = 0

-c + d = 1

Isolating c in the first equation we get:

c = 2d

Replacing that in the other equation we get:

-(2d) + d = 1

-d = 1

d = -1

Then:

c = 2d = 2*(-1) = -2

c = -2

So the values are:

b = 1
a = -1
c = -2
d = -1

If you want to learn more about systems of equations, you can read:

brainly.com/question/13729904

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Lady_Fox [76]

Answer:

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Step-by-step explanation:

V=216cm³

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3 years ago

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Answer:

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Step-by-step explanation:

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