Question

Which expression gives the distance between the points (4, −2) and (4, −5)

Answer 1

No what equation

Answer 2

Which expression gives the distance between the points (4, −2) and (4, −5) ? 
Use the coordinate grid to help you find the answer.
 



(1 point)
Responses

|−5| + |−2|
|−5| + |−2|

|−5| + |4|
|−5| + |4|

|−5| − |−2|
|−5| − |−2|

|−5| − |4|

Answer 3

To find the distance between the points (4, −2) and (4, −5), we can use the distance formula, which is given by:

\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]

In this case, the coordinates of the two points are:
- Point 1: \((x_1, y_1) = (4, -2)\)
- Point 2: \((x_2, y_2) = (4, -5)\)

Now, we can substitute the values into the formula:

\[
d = \sqrt{(4 - 4)^2 + (-5 - (-2))^2}
\]

Calculating the differences:

\[
d = \sqrt{(0)^2 + (-5 + 2)^2}
\]
\[
d = \sqrt{0 + (-3)^2}
\]
\[
d = \sqrt{9}
\]
\[
d = 3
\]

Thus, the distance between the points (4, −2) and (4, −5) is \(3\).

Alternatively, since both points have the same x-coordinate (4), they lie on a vertical line, and the distance can simply be found by calculating the absolute difference between the y-coordinates:

\[
|y_2 - y_1| = |-5 - (-2)| = |-5 + 2| = |-3| = 3
\]

So, the distance is confirmed to be \(3\).

Answer 4

I apologize for the misunderstanding. If you're looking for the expression that represents the distance between the points \((4, -2)\) and \((4, -5)\), here it is:

The general formula for the distance \(d\) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:

\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]

For your specific points, the expression that would give the distance is:

\[
d = \sqrt{(4 - 4)^2 + (-5 - (-2))^2}
\]

This can be simplified to:

\[
d = \sqrt{(0)^2 + (-5 + 2)^2} = \sqrt{(0)^2 + (-3)^2} = \sqrt{9} = 3
\]

So the expression that represents the distance is:

\[
d = \sqrt{(4 - 4)^2 + (-5 + 2)^2}
\]

This equation evaluates to \(3\).

Answer 5

To find the distance between the points \((4, -2)\) and \((4, -5)\) on the coordinate grid, we can write the expression based on the y-coordinates of the points.

The y-coordinates are:
- Point 1: \(y_1 = -2\)
- Point 2: \(y_2 = -5\)

The distance \(d\) can be calculated as the absolute difference between the y-coordinates:

\[
d = |y_2 - y_1| = |-5 - (-2)| = |-5 + 2| = |-3| = 3
\]

Now, looking at the provided options, we can analyze them to find the one that correctly represents this distance:

1. **\(|-5| + |-2|\)**: This does not give the distance between the two points.
2. **\(|-5| + |4|\)**: This also does not give the distance.
3. **\(|-5| - |-2|\)**: This does not provide the correct method for finding distance.
4. **\(|-5| - |4|\)**: This again does not represent the distance.

None of the provided expressions correctly calculate the distance between the points \((4, -2)\) and \((4, -5)\) using the correct method, which is the absolute difference between the y-coordinates.

If we're only looking for one of the provided responses that can approximate the distance calculation, note that the **third option** comes closest by representing a form of operation involving absolute values, but it still does not accurately represent the distance \(d\).

For the absolute distance based purely on the y-coordinates, a closer correct expression should be:

\[
|-5| - |-2| , \text{ or } |y_2 - y_1|
\]

Thus, if forced to select from the given options with the understanding that none fit perfectly, **option 3** \(|-5| - |-2|\) was the closest in terms of mathematical structure to a difference in values, but it's critical to note that it does not equate to the actual distance calculation.