Exploring Distance, Midpoint, & Slope in Real Life

1. A park is located at point A (2, 3) and a playground is at point B (8, 7). Calculate the distance between the two locations using the distance formula.

• 5√2

• 2√13

• √50

• 3√10

Tags

CCSS.HSG.GPE.B.7

3. The midpoint of a line segment connects two stores located at points E (4, 2) and F (10, 6). What is the midpoint of this segment, and what does it represent in this context?

• The midpoint is (7, 4), representing the average location between the two stores.

• The midpoint is (8, 5), representing the average distance to both stores.

• The midpoint is (6, 3), representing the location of a new store.

• The midpoint is (5, 3), representing the closest store to point E.

Tags

CCSS.HSG.GPE.B.6

4. A straight road runs from point G (3, 4) to point H (7, 10). Determine the slope of the road and explain how it might impact driving conditions.

• The slope of the road is 1.0.

• The slope of the road is 1.5.

• The slope of the road is 0.5.

• The slope of the road is 2.0.

Tags

CCSS.8.EE.B.5

5. A delivery truck travels from location I (0, 0) to location J (6, 8). Use the distance formula to find out how far the truck travels. What real-world factors might affect this distance?

• 15

• 10

• 8

• 12

Tags

CCSS.HSG.GPE.B.7

7. A hiking trail runs from point M (2, 3) to point N (10, 15). Calculate the slope of the trail. How might this slope influence the difficulty of the hike?

• 0.5

• 3.0

• 2.0

• 1.5

Tags

CCSS.8.EE.B.5

8. A city planner is designing a new road that connects point O (1, 2) and point P (9, 10). What is the distance between these two points? How can this information be useful for the planner?

• 12

• 10

• 8√2

• 5√2

Tags

CCSS.HSG.GPE.B.7

9. The coordinates of two bus stops are Q (3, 7) and R (7, 3). Find the midpoint of the segment connecting these stops. What does this midpoint indicate about the location of the bus stops?

• (3, 3)

• (4, 6)

• (6, 4)

• The midpoint is (5, 5).

Tags

CCSS.HSG.GPE.B.6

10. A straight path runs from point S (4, 1) to point T (8, 5). Calculate the slope of the path and discuss how it might affect pedestrians using the path.

• The slope of the path is -1.

• The slope of the path is 2.

• The slope of the path is 0.5.

• The slope of the path is 1.

Tags

CCSS.8.EE.B.5