Question

Line segment JK in the xy coordinate plane has endpoints with coordinates (-5,1) and (7,7). What are two possible locations for point m so that m divides JK into two parts with lengths in a ratio of 2:1

Answer 1

the two points would be (-1, 3) and (3, 5)

Explanation:

In order to find this, we need to treat the x-coordinates and y coordinates separately. First let's tackle the x.

X

To find the 2:1 ration marks, first we have to find the difference in the x values.

7 - -5 = 12

So we know they are 12 apart. Now we divide this by 3 and we have the intervals that we can use.

12/3 = 4

So, we know our first ordered pair will come at 4 more than the lower value, and the second will come at 4 less than the highest value.

-5 + 4 = -1

7 - 4 = 3

Now do the same for y values

Y

To find the 2:1 ration marks, first we have to find the difference in the y values.

7 - 1 = 6

So we know they are 12 apart. Now we divide this by 3 and we have the intervals that we can use.

6/3 = 2

So, we know our first ordered pair will come at 4 more than the lower value, and the second will come at 4 less than the highest value.

1 + 2 = 3

7 - 2 = 5

Answer 2

Explanation:

Choose all that apply.

Five characteristics of agrarian societies were _____.

rapid technological advances

less leisure time

extra food during winter

less social organization

freedom to work different jobs

disease did not spread easily

a high-protein diet

depletion of the soil