Question

Three students are standing in a park with signboards 'SAVE ENVIRONMENT', 'DON'T LITTER' and 'KEEP YOUR PLACE CLEAN'. Their positions are marked by the points A(0,7,10), B(-1, 6, 6) and C(-4, 9, 6).

Three students are holdings green colour ribbon together. Does the ribbons form sides or a right angled triangle? Do you feel the need to promote?

What message is given from this question to the society?

Answer 1

Let the points A(0, 7, 10), B(-1, 6, 6) and C(-4, 9, 6) be the vertices of the triangle.

Then, $AB=\sqrt{(0+1{)}^2+(7-6{)}^2+(10-6{)}^2}$ $[\because distance=\sqrt{(x_1-x_2{)}^2+(y_1-y_2{)}^2+(z_1-z_2{)}^2}]$

= $\sqrt{1^2+1^2+4^2}=\sqrt{18}=3\sqrt{2}$

$BC=\sqrt{(-1+4{)}^2+(6-9{)}^2+(6-6{)}^2}=\sqrt{3^2+3^2+0^2}=\sqrt{18}=3\sqrt{2}$

$CA=\sqrt{(-4-0{)}^2+(9-7{)}^2+(6-10{)}^2}=\sqrt{4^2+2^2+4^2}=\sqrt{36}=6$

Now $A{B}^2+B{C}^2=(3\sqrt{2}{)}^2+(3\sqrt{2}{)}^2=18+18=36=6^2=C{A}^2$

Hence, $\Delta ABC$ is right angled triangle at B.

Yes, this question gives us message to protect our environment and help us to follow these in our daily lives to make ourselves healthy.