Respuesta :
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:
[tex]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} }[/tex]
Step 1
use the formula to find the length PQ
Let
P1=P=P(2, −3, −4)
P2=Q=Q(8, 0, 2)
[tex]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\\[/tex]
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)
[tex]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\\[/tex]
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)
[tex]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\\[/tex]
the length PR is 9.48 units
Step 4
is it a right triangle?
you can check this by using:
[tex]side^{2} +side^{2}=hypotenuse ^{2}[/tex]
Let
side 1=side 2= 9
hypotenuse = 9.48
Put the values into the equation
[tex]9^{2} +9^{2} =9.48^{2}\\ 81+81=90\\162=90,false[/tex]
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
