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neonofarm [45]
3 years ago
6

Find the lengths of the sides of the triangle PQR. P(2, −3, −4), Q(8, 0, 2), R(11, −6, −4) |PQ| = Incorrect: Your answer is inco

rrect. |QR| = |RP| = Is it a right triangle? Yes No Is it an isosceles triangle? Yes No
Mathematics
1 answer:
Aloiza [94]3 years ago
3 0

Answer:

the length PQ is 9 units,the length QR is 9 units,the length PR is 9.48 units,the triangle is not a right triangle,this is a isosceles triangle

Step-by-step explanation:

Hello, I think I can help you with this

If  you know two points, the distance between then its given by:

P1(x_{1},y_{1},z_{1} ) \\P2(x_{2},y_{2},z_{2})\\\\d=\sqrt{(x_{2}-x_{1} )^{2} +(y_{2}-y_{1}  )^{2}+(z_{2}-z_{1} )^{2} }

Step 1

use the formula to find the length PQ

Let

P1=P=P(2, −3, −4)

P2=Q=Q(8, 0, 2)

d=\sqrt{(8-2)^{2} +(0-(-3))^{2}+(2-(-4))^{2}} \\ d=\sqrt{(6)^{2} +(3)^{2}+(6 )^{2}}} \\d=\sqrt{36+9+36}\\d=\sqrt{81} \\d=9\\

the length PQ is 9 units

Step 2

use the formula to find the length QR

Let

P1=Q=Q(8, 0, 2)

P2=R= R(11, −6, −4)

d=\sqrt{(11-8)^{2} +(6-0))^{2}+(-4-2 )^{2}}  \\\\\\d=\sqrt{(3)^{2} +(6)^{2}+(-6 )^{2}}} \\d=\sqrt{9+36+36}\\d=\sqrt{81} \\d=9\\

the length QR is 9 units

Step 3

use the formula to find the length PR

Let

P1=P(2, −3, −4)

P2=R= R(11, −6, −4)

d=\sqrt{(11-2)^{2} +(-6-(-3)))^{2}+(-4-4 )^{2}}  \\\\\\d=\sqrt{(9)^{2} +(-6+3)^{2}+(-4-(-4) )^{2}}} \\d=\sqrt{81+9+0}\\d=\sqrt{90} \\d=9.48\\

the length PR is 9.48 units

Step 4

is it a right triangle?

you can check this by using:

side^{2} +side^{2}=hypotenuse ^{2}

Let

side 1=side 2= 9

hypotenuse = 9.48

Put the values into the equation

9^{2} +9^{2} =9.48^{2}\\ 81+81=90\\162=90,false

Hence, the triangle is not a right triangle

Step 5

is it an isosceles triangle?

In geometry, an isosceles triangle is a type of triangle that has two sides of equal length.

Now side PQ=QR, so this is a isosceles triangle

Have a great day

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