Let's determine the coordinate of the point
P given that it lies on the line segment joining the points
(3,2,−1) and
(6,2,−2), with the
x coordinate of
P being 5 .
The coordinates of the point
P that divides the line segment joining
(x1,y1,z1)=(3,2,−1) and
(x2,y2,z2)=(6,2,−2) can be found using the section formula.
Assume
P divides the line segment in the ratio
k:1. Therefore, the coordinates of
P can be represented as:
P(x,y,z)=(‌,‌,‌)Given that the
x coordinate of
P is 5 , we write:
‌=5Plugging
x1=3 and
x2=6 into the equation, we get:
‌=5Solve for
k :
‌6k+3=5(k+1)‌6k+3=5k+5‌6k−5k=5−3‌k=2 Using this value of
k, let's find the
y coordinate of
P :
y=‌Substitute
k=2,y1=2, and
y2=2 :
y=‌=‌=2Therefore, the
y coordinate of
P is 2 . The correct answer is:
Option A: 2