Question

Which expressions are algebraically equivalent to the correct usage of the distance formula to find the distance from point A(3,k) to point B(h,4)?

There is more than one correct answer choice. Select all correct answer choices.

1.(k−h)2+(3−4)2−−−−−−−−−−−−−−−√
2. (k−4)2+(3−h)2−−−−−−−−−−−−−−−√
3.(h−3)2+(4−k)2−−−−−−−−−−−−−−−√
4. (3−h)2+(k−4)2−−−−−−−−−−−−−−−√
5.(4−k)2+(h−3)2−−−−−−−−−−−−−−−√
6.(3−4)2+(k−h)2−−−−−−−−−−−−−−−√
7.(4−3)2+(h−k)2−−−−−−−−−−−−−−−√
8.(h−k)2+(4−3)2

Answer 1

The correct answer is:

2)
`√((k-4)^2+(3-h)^2)`

3)
`√((h-3)^2+(4-k)^2)`

4)
`√((3-h)^2+(k-4)^2)`

5)
`√((4-k)^2+(h-3)^2)`

Explanation:

We can find the distance between two points with the help of the distance formula.

The distance between two points (a,b) and (c,d) is calculated by the formula:

`Distance=√((c-a)^2+(d-b)^2)`

which is similar to the expression:

`Distance=√((-(a-c)^2)+(-(b-d)^2))\\\\i.e.\\\\Distance=√((a-c)^2+(b-d)^2)`

or

`Distance=√((a-c)^2+(d-b)^2)`

or

Distance=\sqrt{(c-a)^2+(b-d)^2}[/tex]

Here we are asked to find the distance between the point A(3,k) and B(h,4)

The distance is given by:

`Distance=√((h-3)^2+(4-k)^2)`

which is also written by:

`Distance=√((h-3)^2+(k-4)^2)`

or

`Distance=√((3-h)^2+(4-k)^2)`

or

`Distance=√((3-h)^2+(k-4)^2)`

Answer 2

(5)

Explanation:

The given two points are:

A(3,k) and B(h,4)

Now, using the distance formula that is=
`\sqrt{(y_(2)-y_(1))^(2)+(x_(2)-x_(1))^(2)}`.

In the given points,
`y_(2)=4`,
`y_(1)=k`,
`x_(2)=h` and
`x_(1)=3`, thus,

`\sqrt{(y_(2)-y_(1))^(2)+(x_(2)-x_(1))^(2)}`=
`\sqrt{(4-k)^(2)+(h-3)^(2)}`

which is the required equation, hence option 5 is correct.