Elements of descriptive geometry, with applications to isometric projection and othe forms of one-plane projection; a text-book for colleges and ingineering schools by O. E. Randall.

RELATING TO POINT, LINE, AND PLANE

59

The distance of a point from a plane is measured on a straight
line drawn from the point perpendicular to the plane. If then we
find the point in which such a line intersects the given plane, the
distance from the given point to this point of intersection will be
the required distance.
Construction. See Fig. 69. Let S represent the given plane and
let O represent the given point. Through o, draw o,-d, perpendicular
to S-s, and through o' draw o'-d' perpendicular to S-s'. 0-D is
the required line.
By Problem 89 find the point D in which the line 0-D intersects
S. The distance 0-D, which is found by revolving the horizontal
projecting plane of 0-D about o,-d, into H (see Problem 72), is
the required distance. o
Check. To test the perpendicu-
larity of the line, draw through D
some line of the plane and note
whether this line is perpendicular to
O-D. To test the distance of the
point from the plane, revolve the
vertical projecting plane of 0-D G S -i.L
about ol-d' into V. \
155. Problem 93. Find the dis- /
tance of the point M=-2, -5,-8
from the plane S = 0~, oc, 2./ \
156. Problem 94. Find the distance of the point M= - 2,- 6,- 6 -
FIG. 69
from the plane S = 0~, 2, oc.
157. Problem 95. Find the distance of the point M1= 0, - 6, - 6
from the plane S = - 4, 300~, 270~.
158. Problem 96. Find the distance of the point M = 0, - 6, - 6
from the plane S = - 4, 270~, 330~.
159. Problem 97. Find the distance of the point M= 0, - 8, 6
from the plane S = 0, 210~, 60~.
160. Problem 98. Find the distance of the point 1 = 0, - 6, - 6
from the plane S = 0~, - 3, - 6.
161. Problem 99. To project a given straight line upon a given
plane.