Question

Find the distance between the points (-3, 11) and (5, 5).

Answer 1

Label the two points (x1,y1) and (x2,y2)

Answer 2

So

x1 = -3, y1 = 11

and

x2 = 5, y2 = 5

Answer 3

Now evaluate

x2 - x1

and tell me what you get

Answer 4

x2 - x1

5 - (-3) ... replace x1 with -3 and x2 with 5

5 + 3

8

See how I got that?

Answer 5

yes

Answer 6

So

(x2-x1)^2 = (8)^2 = 64

Answer 7

Now what about

y2 - y1

???

Answer 8

2

Answer 9

what is y2 ?

Answer 10

2\[\sqrt{10}\]

Answer 11

y2?

Answer 12

The two given points are

(-3, 11) and (5, 5)

In general, they are

(x1,y1) and (x2,y2)

Answer 13

See how y1 matches up with 11 ?

Answer 14

yes

Answer 15

what does y2 match with?

Answer 16

5

Answer 17

so

y2 - y1

5 - 11

-6

Answer 18

Then square it to get (-6)^2 = 36

Answer 19

The next step is to take these squares, 64 and 36, and add them to get

64+36 = 100

Finally, take the square root

sqrt(100) = 10

Answer 20

So the distance between the two points is 10 units

Answer 21

thankyou

Answer 22

You can prove this visually by plotting the two points. Then drawing a circle centered at one point and that passes through the other point. You'll see that the radius of this circle is 10 units.

Answer 23

yw

Answer 24

ok thanks