I have displayed the image for analysis. Now, let's address each of the quiz questions in order.

1. Give two names for the plane.

• Based on the diagram, the plane can be named using three non-collinear points in the plane.
  • Two possible names are:
    • Plane ABC
    • Plane ABD

2. Name three collinear points.

• Collinear points are points that lie on the same straight line.
  • Points A, B, and C are collinear.

3. Name three coplanar points.

• Coplanar points are points that lie on the same plane.
  • Points A, B, and D are coplanar.

4. Name three points.

• You can select any three points from the diagram. For example:
  • Points A, B, and D.

5. Name one ray.

• A ray starts from one point and goes infinitely in one direction.
  • Ray AB (starting at A and passing through B).

6. Name two lines.

• From the diagram, two lines can be named:
  • Line AC
  • Line BD

7. Name one line segment.

• A line segment has two endpoints.
  • Line segment AB.

8. Sketch the figure described: AB and AC.

• This requires drawing the two rays AB and AC, which share the same starting point A and move in different directions.

9. Plane C and plane D intersecting at XY.

• This suggests that two planes intersect at line XY. You can visualize this as a line where two flat surfaces meet.

10. Find BD.

• Based on the work shown on the page, BD is given as 17.

11. The endpoints of $\overline{QR}$ are Q(1,6) and R(7,3). Find the coordinates of the midpoint M.

• To find the midpoint $M(x,y)$ of a segment with endpoints $(x_1, y_1)$ and $(x_2, y_2)$, use the midpoint formula: $M = \left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right)$ Substituting: $M = \left(\frac{1 + 7}{2}, \frac{6 + 3}{2}\right) = (4, 4.5)$ So, the midpoint $M$ is $(4, 4.5)$.

12. Find the distance between the two points S(-5, -2) and T(7, 4).

• Use the distance formula: $d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$ Substituting: $d = \sqrt{(7 - (-5))^2 + (4 - (-2))^2} = \sqrt{(12)^2 + (6)^2} = \sqrt{144 + 36} = \sqrt{180}$ So, $d = \sqrt{180} = 13.42$ (rounded to two decimal places).

13. Identify the segment bisector of $\overline{QR}$.

• The bisector of a segment divides it into two equal parts. Based on the diagram, the bisector seems to be a line passing through the midpoint of $\overline{QR}$.

14. Find the coordinates of endpoint H if the midpoint of $\overline{GH}$ is M(4, -3) and G is (2, 4).

• Use the midpoint formula to find the missing endpoint $H(x_2, y_2)$. We know the midpoint formula is: $M = \left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right)$ For the x-coordinate: $4 = \frac{2 + x_2}{2} \implies 8 = 2 + x_2 \implies x_2 = 6$ For the y-coordinate: $-3 = \frac{4 + y_2}{2} \implies -6 = 4 + y_2 \implies y_2 = -10$ Therefore, the coordinates of $H$ are $(6, -10)$.

Feel free to ask for more details or clarification!

Here are 5 related questions to deepen your understanding:

1. What is the difference between a ray and a line?
2. How do you determine if points are collinear?
3. What is the difference between coplanar and collinear points?
4. How do you find the equation of a line given two points?
5. What is the relationship between the segment bisector and the midpoint?

Tip: Always double-check your substitution in formulas like the distance or midpoint formulas to avoid simple mistakes.