Use the given points to answer the following questions.

a(−4, 0, −8),
b(3, 3, −7),
c(1, 4, 9)

1. which of the points is closest to the yz-plane? a b c
2. which point lies in the xz-plane? a b c

1) C

2) B

Step-by-step explanation:

1) If a point lies ON the yz-plane, no matter what its coordinates are, one thing is for sure that its x-coordinate will always be zero! (this is helpful for visualization).

This information can guides us about which coordinate is responsible for how close or far we are to yz-plane!

The closest point to yz-plane would be the point the smallest value of x-coordinate. regardless of the the side.

here, among A,B, and C. C has the smallest x-coordinate, hence C is closest to the yz-plane.

2) If a point lies on xz plane, no matter what its coordinates are, its y-coordinate will always be zero.

Hence, among A,B, and C. A is the coordinate with y-coordinate as 0. Hence, B lies on the xz-plane.

1. C

2. A

Step-by-step explanation:

Given;

A(−4, 0, −8),

B(3, 3, −7),

C(1, 4, 9)

1. y,z plane lies on the that passes x = 0.

xy-plane = (0,y,z)

Therefore, the point closest to the yz is the point with the lowest absolute x (lowest |x|)

For;

A: |x| = |-4| = 4

B: |x| = |3| = 3

C: |x| = |1| = 1

The lowest |x| = 1 which is C

Therefore, the closest point to the yz axis is C

2. xz-plane is the plane passing through y=0.(xz plane = (x,0,z))

For a point to lie on the xz plane, it most be on y=0 (y coordinate must be equal to 0)

So,

For A: (-4,0,-8) = (x,y,z)

For A : y = 0

Therefore, A lies on the xz plane.