Distances — Quiz 4

Questions in this quiz (9)

1. If city $$X$$ is at $$(3, 8)$$ and city $$Y$$ is at $$(7, 3)$$ on a map where coordinates are in inches and each inch represents $$50$$ miles, how far apart are the cities to the nearest ten miles?

   • 320
   • 400
   • 450
   • 350

2. In the standard $$(x, y)$$ plane, what is the distance in coordinate units between the $$x$$- and $$y$$-intercepts of $$y = 4x - 3$$?

   • $$\frac{\sqrt{153}}{16}$$
   • $$\frac{\sqrt{139}}{16}$$
   • $$\frac{\sqrt{196}}{4}$$
   • $$\frac{\sqrt{153}}{4}$$

3. A rescue boat is located $$20$$ kilometers east and $$30$$ kilometers north of a lighthouse. There is an emergency $$5$$ kilometers south and $$10$$ kilometers west of the lighthouse. How far, in kilometers, is the straight-line distance between the rescue boat and the emergency?

   • $$5\sqrt{85}$$
   • $$\sqrt{35}$$
   • $$35$$
   • $$25$$

4. If the points $$(5,m)$$ and $$(17,n)$$ are 26 units apart, what is $$|m-n|$$?

   • $$\sqrt{266}$$
   • $$2\sqrt{133}$$
   • $$\sqrt{133}$$
   • $$4\sqrt{266}$$

5. Find the distance between two parallel lines:$$y = 2x + 5$$ and $$y = 2x + 10$$

   • $$5$$
   • $$\frac{\sqrt{5}}{5}$$
   • $$\sqrt{5}$$
   • 10

6. Find the distance from point $$P(4,-2)$$ to the line $$2x-y=5$$.

   • $$\sqrt{5}$$
   • $$5$$
   • $$\sqrt{2}$$
   • $$4$$

7. The map is being used to plan a 26-mile marathon. Which of the following plans is the best route for the marathon?

   • Dunkirk → Clearfield → Allentown → Dunkirk
   • Dunkirk → Clearfield → Lake City → Allentown → Dunkirk
   • Dunkirk → Lake City → Clearfield → Dunkirk
   • Dunkirk → Lake City → Allentown → Dunkirk

8. Find the perimeter of the polygon shown on the coordinate plane.

   • 17.13
   • 9.85
   • 7.28
   • 24.77

9. In triangle PQR, the midpoints of sides $$QR$$, $$RP$$, and $$PQ$$ are $$(2,1), (4,6), (-3,2)$$ respectively. Find the coordinates of the three vertices $$P$$, $$Q$$, and $$R$$.

   • $$P=(7,9),\ Q=(3,5),\ R=(10,5)$$
   • $$P=(-1,7),\ Q=(-5,-3),\ R=(9,5)$$
   • $$P=(-10,5),\ Q=(5,4),\ R=(7,5)$$
   • $$P=(-10,7),\ Q=(5,7),\ R=(4,5)$$