Question

NO LINKS OR ANSWERING QUESTIONS YOU DON'T KNOW!!

12. The coordinate grid below represents a town.

a. Curtis's house is at (-4, -6) and Jean's house is at (-4, 3). Plot the plots where Curtis's house and Jean's house are located.

b. Each unit on the grid represents 1 mile. If Curtis can ride his bike at a constant rate of 12 miles per hour, how long would it take Curtis to ride from his house to Jean's house?

THIS IS NOT MULTIPLE CHOICE!!!

Answer 1

9514 1404 393

Answer:

a) see attached

b) 3/4 hour (45 minutes)

Explanation:

a) The attached graph shows the points plotted.

__

b) The points lie on the same vertical line. The distance between them is the difference of their y-coordinates: 3 -(-6) = 9 (miles).

The time is related to distance and speed by ...

time = distance/speed

time = (9 mi)/(12 mi/h) = 9/12 h = 3/4 h

It would take Curtis 3/4 hour to ride from his house to Jean's house.

Answer 2

We are given:

Coordinates of Curtis's house: (-4, -6)

Coordinates of Jean's house: (-4, 3)

a) Plotting these points:

in the given coordinates, the first number is called the abscissa and denotes the x-coordinate of the point.

the second number is the ordinate. it denotes the y-coordinate of the point

Plotting Curtis's house:

We will start from the origin (0,0). move 4 units to the left because that's where x = -4 is.

Then, we will move 6 units downwards and mark the point.

The point we just marked is (-4, -6), Curtis's house

Plotting Jean's house:

We will go to x = -4 like we just did when plotting curtis's house

then, we will move 3 units upwards and mark the point.

This point is (-4, 3), Jean's house

b) Time taken by Curtis:

Distance between the points:

distance =
`√((x_2 - x_1)^2 + (y_2 - y_1)^2)` (distance formula/Pythagoras' Theorem)

where (x₁, y₁) = (-4, -6) and (x₂, y₂) = (-4, 3)

replacing the values in the formula, we get:

distance =
`√((-4 - (-4))^2 + (3 - (-6))^2)`

distance =
`√((0)^2 + (9)^2)`

distance =
`√((9)^2)` = 9 units

since each unit on the grid represents one mile,

distance = 9 miles

speed of Curtis = 12 miles/hour

we know that speed is just (distance covered)/(time taken)

speed = (distance covered)/(time taken)

replacing known values

12 = 9 / time

12 * time = 9 [multiplying both sides by time]

time = 9/12 [dividing both sides by 12]

time = 3/4 hours

time = 0.75 hours OR 45 minutes