Based on the figure, the statements that are true are
- SV is perpendicular to TP
- SV is perpendicular to plane A
- point P lies on SV and in plane A
That is, the first, second and fifth statements.
From the image, we will determine the statements that are true based on the figure.
For the first statement - SV is perpendicular to TP
From the figure,
SV is a line intersecting plane A at point P, at right angle. That is, SV is perpendicular to point P. Then, SV is perpendicular to plane A since point P lies on the plane.
Also, P lies on the plane (plane A); then we can infer that TP is parallel to plane A since point T also lie on the plane (plane A).
Since, SV is perpendicular to the plane, then SV is also perpendicular to TP.
∴ The statement (SV is perpendicular to TP) is true
For the second statement - SV is perpendicular to plane A
As stated above, SV is perpendicular to point P. Since point P lies on the plane (plane A), then SV is perpendicular to plane A.
∴ The statement (SV is perpendicular to plane A) is true
For the third statement - points S, P and Q are collinear
Collinear points are points that lie on the same line.
Points S, P and Q are not collinear because, a single line cannot pass through the three points, that is, the points (S, P, and Q) do not lie on a single line.
∴ The statement (points S, P and Q are collinear) is NOT true
(From the image, an example of points that are collinear are points S, P, and V)
For the fourth statement - points R, T, and U are collinear
As explained above, points R, T, and U are not collinear because, a single line cannot pass through the three points, that is, the points (R, T, and U) do not lie on a single line.
∴ The statement (points R, T and U are collinear) is NOT true
NOTE: (The points only lie in the same plane (plane A), that is, they are coplanar)
For the fifth statement - point P lies on SV and in plane A
Since line SV intersects plane A at point P, that means point P lies in plane A. Also point P lies on line SV since it is on the line as shown in the image.
∴ The statement (point P lies on SV and in plane A) is true
For the sixth statement - points U, S, V, and Q are coplanar
Points or lines are said to be coplanar if they lie in the same plane.
Of the given points, only point U lies in plane A. Points S, V, and Q do not lie in the same plane and as well do not lie in the same plane as point U.
∴ The statement (points U, S, V, and Q are coplanar) is NOT true.
(From the image, an example of points that are coplanar are points U,P,R, and T because they lie on the same plane).
Hence, based on the figure, the statements that are true are the first, second and fifth statements. that is
- SV is perpendicular to TP
- SV is perpendicular to plane A
- point P lies on SV and in plane A
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