Question

Find the coordinates of the points which trisect the line segment joining the points
P (4.2.-6) and Q (10.-16, 6).​

Answer 1

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Answer 2

Answer:

Step-by-step explanation:

P-----------S------------R ----------------Q

Let S and R in such a way that

PS = SR = RQ

Hence, S divides the Line PQ in the ratio 1 : 2 and R divides the Line in the ratio 2 : 1

Now, use section formula ,

(x, y, z )≡ { (mx₂ + nx₁)/(m + n), (my₂ + ny₁)/(m + n), (mz₂ + nz₁)/(m + n)}

For point S ,

m : n = 1 : 2 and (x₁ , y₁ , z₁ ) = ( 4, 2 , -6) and ( x₂ , y₂ , z₂) = (10, -16, 6)

S ≡ { ( 1 × 10 + 2 × 4 )/(1 + 2), ( 1 × -16 + 2 × 2)/(1 + 2) , ( 1 × 6 + 2 × -6)/(1 + 2)}

S ≡{ (10 + 8)/3, ( -16 + 4)/3, ( 6 -12)/3 }

S≡ ( 6, -4, -2 )

For point R ,

m : n = 2 : 1 , (x₁ , y₁ , z₁ ) = ( 4, 2 , -6) and ( x₂ , y₂ , z₂) = (10, -16, 6)

R ≡ {2 × 10 + 1 × 4)/3 , ( 2 × -16 +1 × 2 )/3, ( 2 × 6 + 1 × -6 )/3 }

R ≡ { (20 + 4)/3 , ( -32 + 2)/3, ( 12 - 6)/3, }

R≡ ( 8, -10, 2 )

Hence, required points are ( 6, -4, -2) and ( 8, -10, 2)

Hope it helps you.