Question

3. What is the length of the segment joining the points at (–3, 0) and (5, 6)?
_________ units

4. What is the length of the segment joining the points at (1, –8) and (5, 0)?
Round to the nearest tenth if necessary.
_________ units

Answer 1

@jdoe0001 @TheSmartOne

Answer 2

\(\bf \textit{distance between 2 points}\\ \quad \\
\begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
% (a,b)
&({\color{red}{ -3}}\quad ,&{\color{blue}{ 0}})\quad
% (c,d)
&({\color{red}{ 5}}\quad ,&{\color{blue}{ 6}})\\
% (a,b)
&({\color{red}{ 1}}\quad ,&{\color{blue}{ -8}})\quad
% (c,d)
&({\color{red}{ 5}}\quad ,&{\color{blue}{ 0}})
\end{array}\qquad
% distance value
d = \sqrt{({\color{red}{ x_2}}-{\color{red}{ x_1}})^2 + ({\color{blue}{ y_2}}-{\color{blue}{ y_1}})^2}\)

Answer 3

so their "distance" is also their "length

Answer 4

well. the length of the segment between them for that matter

Answer 5

I'm still confused, can you put it any simpler?

Answer 6

@jdoe0001 @TheSmartOne@jim_thompson5910 @e.mccormick @Data_LG2 @dan815

Answer 7

You plug in the points into the formula and solve for the distance.

Answer 8

So for right now, lets consider these 2 points \(\sf (3, 0) ~and ~(5, 6)\)

So using the formula
\(\Large\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

And the points are in the form of \(\sf(x_1,y_1),(x_2,y_2)\)

Answer 9

And so then

\(\sf x_1 = 3 \\ x_2 =5 \\y_1=0 \\y_2=6\)

And then just plug it in to the huge distance formula :)

Answer 10

Can you help me fill in the formula?

Answer 11

\(\large\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

\(\sf x_1 = 3 \\ x_2 =5 \\y_1=0 \\y_2=6\)

\(\large\sqrt{(5-3)^2+(6-0)^2}\)

Answer 12

2√10?

Answer 13

Correct :)

Answer 14

For the second question :P

\(\large\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

\(\sf x_1 = 1 \\ x_2 =5 \\y_1=-8 \\y_2=0\)

\(\large\sqrt{(5-1)^2+(0-(-8))^2}\)

Answer 15

But for the first one how many units would that be?

Answer 16

It would just be \( 2\sqrt{10}\) units

Answer 17

But I can put that symbol in...

Answer 18

1. 2√10
2. 4√5

Answer 19

That is correct.

If it doesn't allow you to put that symbol.. then we could simplify that and then

1)6.325
2)8.944

That is what you would get if you plugged it into the calculator and rounded upto 3 digits.

Answer 20

Thank you. :)

Answer 21

Np :)