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oksano4ka [1.4K]
3 years ago
5

. Do the points P (-2, -3), Q (4, 1) and R (2, 4) form a right triangle?

Mathematics
1 answer:
FrozenT [24]3 years ago
3 0

Answer:

Since the length of the sides respects the Pythagorean theorem, these points form a right triangle.

Step-by-step explanation:

Distance between two points:

Suppose that we have two points, (x_1,y_1) and (x_2,y_2). The distance between them is given by:

D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}

Right triangle:

Sum of the squares of the two smaller sides is equal to the square of the largest side(Pythagorean theorem).

Length of side PQ:

P (-2, -3), Q (4, 1)

a = \sqrt{(4 - (-2))^2+(1 - (-3))^2} = \sqrt{6^2 + 4^2} = \sqrt{52}

Length of side PR:

P (-2, -3), R (2,4)

b = \sqrt{(2 - (-2))^2+(4 - (-3))^2} = \sqrt{4^2 + 7^2} = \sqrt{65}

Length of side QR

Q (4, 1), R (2,4)

c = \sqrt{(2 - 4)^2+(4 - 1)^2} = \sqrt{2^2 + 3^2} = \sqrt{13}

Pythagorean Theorem:

Smaller sides: a and c

Largest side: b

So

a^2 + c^2 = b^2

(\sqrt{52})^2 + (\sqrt{13})^2 = (\sqrt{65})^2

52 + 13 = 65

65 = 65

Since the length of the sides respects the Pythagorean theorem, these points form a right triangle.

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slega [8]

Answer:

m<6 = 130°

Step-by-step explanation:

If m∠2 = 130°, what is m∠6?

Find the diagram attached

From the digram we can see that the vertical lines are parallel. Hence based on geometry;

m<2 = m<6 (corresponding angles)

Given m<2 = 130°, hence m<6 = 130°

8 0
3 years ago
A picnic basket was marked up 95% from an original cost of $9.57. Last Friday, Rosanne bought the picnic basket and paid an addi
Montano1993 [528]

Answer:

$20.15

Step-by-step explanation:

Given data

Original cost =  $9.57

Markup= 95%

Let us find the new cost of the basket

=95/100*9.57

=0.95*9.57

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Hence the cost of the basket is

= 9.57+9.0915

=18.66

Also, the sales tax is 8%

=8/100*18.66

=0.08*18.66

=1.4928

Therefore, the total amount to be paid is

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8 0
3 years ago
Which of the following functions best represents the graph?
Leviafan [203]
I believe the answer is B.
4 0
3 years ago
Read 2 more answers
What 2 numbers equal -36 when multiplied together but equal 0 when added together?
Lelu [443]
You can do that using  +6  and  -6 .

(6) · (-6)  =  - 36

(6) + (-6)  =  0
7 0
3 years ago
14
Arada [10]

Answer:

Gerrard

Step-by-step explanation:

Let the size of each poster be x

Eve's poster portion painted will be

=\frac{1}{6}\times x\\=\frac{x}6}

Gerrard's painted portion will be:

=\frac{1}{5}\times x\\=\frac{x}{5}

From the two inequalities, we find that \frac{x}{5} is greater than \frac{x}{6}  by x/30

\frac{x}{5}-\frac{x}{6}\\=\frac{x}{30}\\

hence Gerrard has the larger blue section. His portion is 16.67% greater than Eve's

6 0
3 years ago
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