Geometry, Homework Practice Workbook 1st Edition Chapter 1 Points Lines and Planes
Page 1 Problem 1 Answer
Given,
We need to name a line that contains point E.
Given,
By watching the picture, we can clearly say that the name of the line that contains point E is the line q or EB or BE.
The name of the line that contains point E is the line q or EB or BE.
Page 1 Problem 2 Answer
Given,
We need to name a point contained in line n.
Given,
By watching the picture, we can clearly say that the point contained in line n is A or B.
The point contained in line n is A or B.
Page 1 Problem 3 Answer
Given,
We need to determine another name for line P.
Given,
By watching the picture, we can clearly say that the other name for line p is CDor DC.
The other name for line p is CD or DC.
Page 1 Problem 4 Answer
Given.
We need to name the plane containing lines n and p.
Given,
By watching the picture, we can clearly say that the name of the plane containing n and p is plane G.
The name of the plane containing n and p is plane G.
Page 1 Problem 5 Answer
We need to draw and label a figure on the basis of the given information, the point K lies on RT.
Given information, the point K lies on RT.
The drawn figure –
In the picture, the dark dots represent points, the arrow represents a line, and the page represents a plane.
The drawn figure –
In the picture, the dark dots represent points, the arrow represents a line, and the page represents a plane.
Page 1 Problem 6 Answer
We need to draw and label a figure on the basis of the given information, YP
lies in plane B and contains point C but does not contain point H.
Given information, YP lies in plane B and contains point C, but does not contain point H.
The drawn figure –
In the picture, the dark dots represent points, the arrow represents a line, and the page represents a plane.
The drawn figure –
In the picture, the dark dots represent points, the arrow represents a line, and the page represents a plane.
Page 1 Problem 7 Answer
We need to draw and label a figure on the basis of the given information, line q and f intersect at point Z in-plane U.
Given information, line q and f intersect at point Z in-plane U.
The drawn figure –
In the picture, the dark dots represent points, the arrow represents a line, and the page represents a plane.
According to the given information, the figure is,
Page 1 Problem 8 Answer
Given,
We need to determine how many planes are shown in the figure.
Given,
By watching the picture, we can say that the planes are ABC, FED, EBC, DFA, AFB. So the number of planes in the figure is 5.
After briefly examining the picture, we came to the conclusion that there are 5 planes in the figure.
Page 1 Problem 9 Answer
Given,
We need to determine how many planes contains the points F and E.
Given,
By watching the picture, we can clearly say that the number of planes contains F and E is 2.
The number of planes contains F and E is 2.
Page 1 Problem 10 Answer
Given,
We need to determine four points that are co-planar.
Given,
By watching the picture, we can clearly say that the co-planer points are E, B, C, and D.
The co-planer points are E, B, C, and D.
Page 1 Problem 11 Answer
Given,
We need to determine whether points A, B and C are coplanar or not.
Given,
We know, Co-planer points, mean points situated in the same plane.
So, points A, B, and C are coplanar.
Because they are situated in the same plane.
So, points A, B, and C are coplanar.
Because they are situated in the same plane.
Page 2 Problem 12 Answer
Given,
We need to name a line that contains points T and P.
Given,
By watching the picture, we can clearly say that the line containing points T and P is line g or TP or TN or NP.
The containing points T and P is line g or TP or TN or NP.
Page 2 Problem 13 Answer
Given,
We need to determine a line that intersects the plane containing points Q, N, and P.
Given,
By watching the picture, we can say that the line that intersects the plane containing points Q.N, and P is line J or MT.
The line that intersects the plane containing points Q, N, and P is line J or MT.
Page 2 Problem 14 Answer
Given,
We need to determine the plane that contains TN and QR.
Given.
By watching the picture, we can clearly say that the plane contains TN and QR is plane S.
The plane contains TN and QR is plane S.
Page 2 Problem 15 Answer
The given relation is, two lines AK and CG intersect at a point M in plane T.
We draw these two lines in a plane where these lines have different slopes i.e. they are not parallel as they intersect at a particular point.
We have the conditions, two lines AK and CG intersect at a point M in the plane T.
Now, first, we draw a plane T as
Now we draw two lines AK and CG on this plane, where they are not parallel.
The two lines intersect at a point that is labeled as M.
Finally, we can conclude that the given relation can be drawn and labeled as
Page 2 Problem 16 Answer
The given relation is, a line contains L(-4,-4) and M(2,3). Line q is in the same coordinate plane N but does not intersect the line LM.
The N plane is given as the X-Y plane.
We draw a line that passes through both the given points.
Then we make another line q in the same plane N(x-y) in such a way that it is parallel to LM i.e. they do not intersect.
We have the conditions, one line that connects the two points L(−4,−4) and M(2,3).
First, we draw a line LM through these two points in the N plane (X-Y).
Then we draw a random line in parallel with LM so that they do not intersect with each other.
Finally, we can conclude that the given relation can be drawn and labeled as
Page 2 Problem 17 Answer
We are given a figure,
and we have to find the number of planes in this figure.
From this figure, we can find that the planes are, WPQT, WPNM, TQRS, QPNR, TWMS, and also MNSR that is coinciding in plane A.
We can figure out there are 6 planes in the given figure.
Finally, we can conclude that the given figure has 6 planes.
Page 2 Problem 18 Answer
We have the given figure,
and we have to find three collinear points.
Now, in the whole figure, we can see only one case where three points M, X, and S are in the same line.
Therefore, M, X, S are collinear points.
Finally, we can conclude that the three collinear points are M, X, and S.
Page 2 Problem 19 Answer
We are given the figure,
and we have to check whether N, R, S, and W are coplanar or not.
We know, that for being coplanar these points have to be on the same plane.
Now, we can see that N, R, and S are in the same plane i.e. plane A, but point W is not in the same plane.
Therefore, the points N, R, S, and W are not coplanar.
Finally, we can conclude that the given points N, R, S, and W are not coplanar.
Page 2 Problem 20 Answer
We are given the figure,
Now, we can clearly see, that the strings are connected between two points and also it is straight and one-dimensional, hence the string models Lines.
Finally, we can conclude that the strings model Lines.
Page 2 Problem 21 Answer
We are given the reference of a car antenna,
Now, we can clearly see, that the antenna is a one-dimensional linear structure i.e. referring to a Line and the tip of the antenna is an exact location, hence models a Point.
Finally, we can conclude that the car antenna models a Line and a Point.