Question

If a point C with y coordinate 2, lies on the line joining the points A(-1, -4, 5) and B(4, 6, -5), then find the coordinates of C.

• A. (2, 2, -1)
• B. (2, 1, 2)
• C. (2, 0, 0)
• D. (0, 2, 4)

Answer 1

Answer: (A)

(2, 2, -1)

Line joining $A(-1,-4,5)$ and $B(4,6,-5)$ is

$\frac{x-4}{-1-4}=\frac{y-6}{-4-6}=\frac{z-(-5)}{5-(-5)}\frac{x-4}{-5}=\frac{y-6}{-10}=\frac{z+5}{10}\Rightarrow \frac{x-4}{1}=\frac{y-6}{2}=\frac{z+5}{-2}=r$

$\therefore$ general c-ordinates of a point on this line is,

$(x,y,z)=(r+4,2r+6,-2r-5)$

y co-ordinates is given as$2\Rightarrow y=2\therefore 2r+6=2\Rightarrow r=-2$

$\therefore (x,y,z)=(2,2,-1)$

Answer A