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3 years ago

15

What is the scale factor of the two triangles below?

1 answer:

irina [24]3 years ago

8 0

The correct answer is: [A]: " $\frac{3}{4}$ " .
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<u>Note</u>: "3/4" = "6/8" = "15/20" .
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Find the length of each side of the triangle determined by the three points P1,P2, and P3. State whether the triangle is an isos

Tanya [424]

Answer:

The triangle is both an Isosceles triangle and a right triangle.

Step-by-step explanation:

Given the vertices of a triangle.

$P_{1} = (- 1, 4)$

$P_{2} = (6, 2)$ and

$P_{3} = (4, - 5)$

We find the distance between all the points to determine the length of each side of the triangle.

Distance between any two points, say, $(x_1, y_1)$ and $(x_2, y_2)$ is:

$\sqrt{\bigg ( \textbf{x}_{\textbf{2}} \hspace{1mm} \textbf{- x}_{\textbf{1}} \bigg )^{\textbf{2}} \textbf{+} \bigg( \textbf{y}_{\textbf{2}} \hspace{1mm} \textbf{- y}_{\textbf{1}} \bigg)^ {\textbf{2}}$

Length between $P_1$ and $P_{2}$ , (Side 1) :

$(x_1, y_1) = (- 1, 4)$ and

$(x_2, y_2) = (6, 2)$

Distance = $\sqrt{\bigg(6 - (-1) \bigg)^{2} \hspace{1mm} + \hspace{1mm} \bigg( 2 - 4 \bigg )^2$

$= \sqrt{7^2 + 2^2}$

$= \sqrt{49 + 4}$

$= \sqrt{\textbf{53}}$

Length of Side 1 = $\sqrt{\textbf{53}}$ units.

Distance between $P_1$ and $P_2$ , (Side 2):

$(x_1, y_1) = (-1, 4)$

$(x_2, y_2) = (4, - 5)$

Distance = $\sqrt{ \bigg( 4 + 1 \bigg)^2 \hspace{1mm} + \bigg( - 5 - 4 \bigg ) ^2$

$= \sqrt{ 25 + 81 }$

$= \sqrt{\textbf{106}}$

Length of Side 2 = $\sqrt{\textbf{106}}$ units.

Distance between $P_2$ and $P_3$ , Side 3 :

$(x_1, y_1) = (4, 5)$

$(x_2, y_2) = (6, 2)$

Distance = $\sqrt{ 2^2 \hspace{1mm} + \hspace{1mm} 7^2}$

$= \sqrt{49 + 4}$

$= \sqrt{\textbf{53}$

Length of Side 3 = $\sqrt{\textbf{53}}$ units.

Note that the length of Side 1 = Length of Side 3.

That means the triangle is Isosceles.

Also, For a triangle to be right angle triangle, using Pythagoras theorem we have:

(Side 1)² + (Side 3)² = (Side 2)²

$\bigg( \sqrt{53} \bigg )^2 \hspace{1mm} + \hspace{1mm} \bigg( \sqrt{53} \bigg)^2 \hspace{1mm} = \hspace{1mm} \bigg ( \sqrt{106} \bigg ) ^2$

i.e, 53 + 53 = 106

Hence, the triangle is a right - angled triangle as well.

7 0

3 years ago

Can you guys help me asap

stepladder [879]

The answer should be D.

7 0

3 years ago

Can you help please?<br><br>

Vilka [71]

In 2 hours,hope this helps :)

7 0

3 years ago

Arrange the steps to solve the equation square root x+3 - square root 2x-1=-2

stiv31 [10]

Answer:x=31.4919

Step-by-step explanation:

Step1:isolate a square root on the left hand side√x+3=√2x-1-2

Step2:eliminate the radicals on the left hand side

Raise both sides to the second power

√x+3)^2=(√2x-1-2)^2

After squaring

x+3=2x-1+4-4-4√2x-1

Step3:get the remaining radicals by itself

x+3=2x-1+4-4√2x-1

Isolate radical on the left hand side

4√2x-1=-x-3+2x-1+4

4√2x-1=x

Step4:eliminate the radicals on the left hand side

Raise both side to the second power

(4√2x-1)^2=x^2

After squaring

32x-16=x^2

Step 5:solve the quadratic equation

x^2-32x-16

This equation has two real roots

x1=32+√960/2=31.4919

x2=32-√960/2=0.5081

Step6:check that the first solution is correct

Put in 31.4919 for x

√31.4919+3=√2•31.4919-1-2

√34.492=5.873

x=31.4919

Step7:check that the second solution is correct

√x+3=√2x-1-2

Put in 0.5081 for x

√0.5081+3=√2•0.5081-1-2

√3.508=-1.873

1.873#-1.873

One solution was found

x=31.4919

6 0

3 years ago

PLEASE HELP ME <br><br><br><br> Find the slope and y-intercept of the following graph.

Ronch [10]

The y-intercept is 2 and the Slope is 2/4 but if you simplify that, it will be 1/2.

8 0

3 years ago