A point C with z-coordinate 8 lies on the line segment joining the points A(2, -3, 4) and B(8, 0, 10). Find the coordinates.

Asked by Sakshi | 1 year ago |  36

##### Solution :-

Given:

The points A (2, -3, 4) and B (8, 0, 10)

Let Point C(x, y, 8), and C divides AB in ratio k: 1

So, m = k and n = 1

A(2, -3, 4) and B(8, 0, 10)

Coordinates of C are: On comparing we get,

$$\dfrac{ [10k + 4] }{ [k + 1]}$$ = 8

10k + 4 = 8(k + 1)

10k + 4 = 8k + 8

10k – 8k = 8 – 4

2k = 4

k = $$\dfrac{4}{2}$$

= 2

Here C divides AB in ratio 2:1

x =$$\dfrac{ [8k + 2] }{ [k + 1]}$$

=$$\dfrac{ [8(2) + 2] }{ [2 + 1]}$$

=$$\dfrac{[16 + 2] }{ }$$

$$\dfrac{18}{3}$$

= 6

y = $$\dfrac{-3 }{ [k + 1]}$$

=$$\dfrac{-3 }{ [2 + 1]}$$

$$\dfrac{-3}{3}$$

= -1

The Coordinates of C are (6, -1, 8).

Answered by Aaryan | 1 year ago

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