Answer:
1. The values of |PQ|, |QR| and |RP| are 3, 3√5 and 6 respectively.
2. No.
3. No.
Step-by-step explanation:
The vertices of given triangle are P(0, 1, 5), Q(2, 3, 4), R(2, −3, 1).
Distance formula:
[tex]D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2}[/tex]
Using distance formula we get
[tex]|PQ|=\sqrt{(2-0)^2+(3-1)^2+(4-5)^2}=\sqrt{9}=3[/tex]
[tex]|QR|=\sqrt{(2-2)^2+(-3-3)^2+(1-4)^2}=\sqrt{45}=3\sqrt{5}[/tex]
[tex]|RP|=\sqrt{(0-2)^2+(1-(-3))^2+(5-1)^2}=\sqrt{36}=6[/tex]
The values of |PQ|, |QR| and |RP| are 3, 3√5 and 6 respectively.
In a right angled triangle the sum of squares of two small sides is equal to the square of third side.
[tex](3)^2+(3\sqrt{5})^2=54\neq 6^2[/tex]
Therefore PQR is not a right angled triangle.
In an isosceles triangle, the length of two sides are equal.
The measure of all sides are different, therefore PQR is not an isosceles triangle.
