Question

geometry: cc.2.3.hs.a.14 common district assessment - unit 1
learning target 3: i can determine and use properties of collinear and coplanar points.
for questions 1-2, use figure 1.

1. which planes contain point w? select all that apply.

a) plane b
b) plane vwy
c) plane vwx
d) plane m
e) plane ryv
f) plane vwz

1. which three points are collinear? select all that apply.

a) points w, x, and r
b) points x, r, and z
c) points w, v and y
d) points x, y, and r
figure 1. image of a plane with lines and points: x, y, w, v on line n; x, y, r on line m; r, z on line ℓ; plane b

Explanation:

Question 1

• Plane B: The figure shows a plane labeled B, and point W is on this plane (since the plane contains the lines and points like W, Y, V, etc. on it).
• Plane VWY: Points V, W, Y are colinear (on line n), so they define a plane (a plane can be defined by three non - colinear points, but here since they are colinear, the line n lies on plane VWY and plane B, and W is on this line, so W is in plane VWY).
• Plane VWX: Wait, looking at the figure, line n has V, W, Y and line m has X, Y, R. Plane VWX would need to contain V, W, X. But X is on line m (perpendicular? No, X is on the horizontal line m with Y and R). Wait, actually, plane B is the large plane. Plane VWY: V, W, Y are on line n, so the plane containing line n and maybe other lines? Wait, re - examining:
• Plane B: The entire flat surface, so W is on Plane B (A is correct).
• Plane VWY: Since V, W, Y are on the same line (line n), they lie on a plane (B is correct).
• Plane VWX: Does X, V, W lie on a plane? X is on line m (with Y, R), V, W, Y on line n. So X, V, W are not colinear and do they lie on a plane? Maybe not. Wait, Plane m: Plane m is the horizontal plane? Wait, the figure has line m (horizontal) and line n (vertical) on plane B. Plane m: line m is on plane B, but W is on line n, not line m. Wait, maybe I misread. Let's re - analyze:
• Plane B: The big plane, so W is on it (A correct).
• Plane VWY: V, W, Y are on line n, so they are coplanar (B correct).
• Plane VWX: No, X is on line m, V, W on line n, so not on the same plane.
• Plane m: Line m is on plane B, but W is on line n, not line m, so W not in Plane m (D incorrect).
• Plane RYV: R is on line m, Y, V on line n. Do R, Y, V lie on a plane? R, Y are on line m and line n (intersection at Y), so R, Y, V are coplanar? Wait, Y is the intersection of line m and line n. So R (on m), Y (on both), V (on n) are coplanar. But does W lie on plane RYV? W is on line n between Y and V, so yes! Because line n is part of plane RYV (since Y, V, R are in the plane, and line n contains Y and V, so W is on line n, hence in plane RYV (E correct).
• Plane VWZ: Z is below the plane B, on line ℓ. W is on plane B, Z is not, so W not in plane VWZ (F incorrect).

So the correct options are A, B, E.

• Option A: Points W, X, and R: W is on line n, X and R are on line m. Line n and line m intersect at Y, so W, X, R are not colinear.
• Option B: Points X, R, and Z: X and R are on line m (horizontal), Z is on line ℓ (vertical through R). So X, R, Z are not colinear (X - R is horizontal, R - Z is vertical).
• Option C: Points W, V and Y: W, V, Y are on line n (the vertical line with arrow down, passing through Y, W, V), so they are colinear.
• Option D: Points X, Y, and R: X, Y, R are on line m (the horizontal line with arrow left and right, passing through X, Y, R), so they are colinear.

Answer:

A. Plane B, B. Plane VWY, E. Plane RYV

Question 2