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3 years ago

Can someone please check my answer?!

Mathematics

1 answer:

Vlad1618 [11]3 years ago

5 0

Answer:

You answered it correctly :)

Step-by-step explanation:

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P1= (5,-4); p2=(8,-3);p3=(7,-10) find the length of each side of the triangle determined by three points

Dima020 [189]

so the points are, from P1 to P2, namely P1P2, and from P2 to P3, namely P2P3, and from P3 back to P1, namely P3P1.

$\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ P1(\stackrel{x_1}{5}~,~\stackrel{y_1}{-4})\qquad P2(\stackrel{x_2}{8}~,~\stackrel{y_2}{-3})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ P1P2=\sqrt{[8-5]^2+[-3-(-4)]^2}\implies P1P2=\sqrt{(8-5)^2+(-3+4)^2} \\\\\\ P1P2=\sqrt{3^2+1^2}\implies \boxed{P1P2=\sqrt{10}}\\\\[-0.35em] \rule{34em}{0.25pt}$

$\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ P2(\stackrel{x_2}{8}~,~\stackrel{y_2}{-3})\qquad P3(\stackrel{x_2}{7}~,~\stackrel{y_2}{-10}) \\\\\\ P2P3=\sqrt{[7-8]^2+[-10-(-3)]^2}\implies P2P3=\sqrt{(7-8)^2+(-10+3)^2} \\\\\\ P2P3=\sqrt{(-1)^2+(-7)^2}\implies P2P3=\sqrt{50}\implies \boxed{P2P3=5\sqrt{2}}\\\\[-0.35em] \rule{34em}{0.25pt}$

$\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ P3(\stackrel{x_2}{7}~,~\stackrel{y_2}{-10})\qquad P1(\stackrel{x_1}{5}~,~\stackrel{y_1}{-4}) \\\\\\ P3P1=\sqrt{[5-7]^2+[-4-(-10)]^2}\implies P3P1=\sqrt{(5-7)^2+(-4+10)^2} \\\\\\ P3P1=\sqrt{(-2)^2+6^2}\implies P3P1=\sqrt{40}\implies \boxed{P3P1=2\sqrt{10}}$

5 0

3 years ago

Need help asap !!!!!

Romashka [77]

Answer:

The answer is x = 5.

Step-by-step explanation:

Given:

Δ ABC is an Isosceles triangle with AB = CA

m∠ ABC = ( 6x + 4 )°

m∠ BAC = 73°

m∠ BCA = ( 8y - 7 )°

To Find:

x = ?

Solution:

Properties of an Isosceles Triangle.

Base angles or two angles are equal.
Any two sides are equal.

Here , Δ ABC is an Isosceles triangle with AB = CA

∴ m∠ BAC = m∠ BCA

$73= 8y-7\\8y=73+7\\8y=80\\y=\frac{80}{10} \\y=10$

∴ m∠ BCA = ( 8y - 7 )°

= 8 × 10 - 7

m∠ BCA = 73 Which is same as ∠ CAB

Property of a Triangle is Sum of the measures of the angle of a triangle is 180°.

$\angle ACB + \angle CAB + \angle CBA = 180$

Substituting the values we get,

$73 + 73 + (6x+4) = 180\\6x+4=180-146\\6x=34-4\\6x=30\\x=\frac{30}{6} \\x=5\\$

The answer is x = 5.

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3 years ago

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1/4.

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Answer:

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