Question

1. use the diagram to answer the following questions.

a) how many points appear in the figure? __
b) how many lines appear in the figure? __
c) how many planes appear in the figure? __
d) name a line containing point v. __
e) name the intersection of lines a and b. __
f) give another name for line b. __
g) name three non - collinear points. __
h) give another name for plane d. __
name: date: 9/03/25 per: __ unit 1: geometry basics homework 1: points, lines, and planes

Explanation:

Step1: Count visible points

We count the distinct points in the figure. There are 5 points: \(V\), \(W\), \(X\), \(Y\), \(Z\).

Step2: Count visible lines

We identify the lines. Lines are \(a\), \(b\), \(VW\), \(XY\), \(WZ\), so there are 5 lines.

Step3: Count visible planes

The whole - surface shown represents plane \(D\), so there is 1 plane.

Step4: Find line with point \(V\)

Line \(a\) contains point \(V\).

Step5: Find intersection of \(a\) and \(b\)

Lines \(a\) and \(b\) intersect at point \(W\).

Step6: Rename line \(b\)

Line \(b\) can also be named line \(WZ\) (using two points on the line).

Step7: Find non - collinear points

Points \(V\), \(X\), \(Y\) are non - collinear (not on the same line).

Step8: Rename plane \(D\)

Plane \(D\) can also be named plane \(VWXYZ\) (using non - collinear points on the plane).

Answer:

a) 5
b) 5
c) 1
d) Line \(a\)
e) Point \(W\)
f) Line \(WZ\)
g) Points \(V\), \(X\), \(Y\)
h) Plane \(VWXYZ\)