Answer:
Hey
Step-by-step explanation:
Im tryna answer this but it don’t let me
Answer:
(C) reflection on y = -x
Step-by-step explanation:
There are vertices on the x-axis, the y-axis, and the line y=x (point Q(3, 3)), so reflection on any of those lines will result in a point being invariant. The only line of reflection among the choices given that does not contain a vertex of the figure is y = -x.
reflection on y = -x will give no invariant points
Answer:
1/6 cubic unit
Step-by-step explanation:
Each plane describes the boundary of a triangular pyramid in the first octant. If we consider the x-y plane to be the base, that base will have an area that is 1/2 the product of the x- and y-intercepts. The height of the pyramid will be the z-intercept, so the volume is ...
V = (1/3)Bh = (1/3)((1/2)(x-intercept)(y-intercept))(z-intercept))
= (1/6)(x-intercept)(y-intercept)(z-intercept)
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We can write the equation of each plane in intercept form by dividing by the constant on the right:
x/(x-intercept) + y/(y-intercept) + z/(z-intercept) = 1
1st plane: x/1 + y/1 + z/1 = 1 . . . . . enclosed volume = (1/6)(1)(1)(1) = 1/6
2nd plane: x/1 + y/1 + z/2 = 1 . . . enclosed volume = (1/6)(1)(1)(2) = 2/6
The difference between the volumes enclosed by the planes is the volume of the region between them, so is ...
V = (2/6) -(1/6) = 1/6 . . . . cubic units
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We note that the x- and y-intercepts of both planes are the same, so the volume is that of a triangular wedge having an edge on the line x+y=1 in the plane z=0.
