Calculating the Distance Between Two Points

To find the distance between the points (-5, -10) and (2, 4), we can use the distance formula:

[

d = sqrt{(x_2 – x_1)^2 + (y_2 – y_1)^2}

]

Where ((x_1, y_1) = (-5, -10)) and ((x_2, y_2) = (2, 4)).

Now, let’s plug in the values:

1. Calculate (x_2 – x_1):

[

2 – (-5) = 2 + 5 = 7

]

2. Calculate (y_2 – y_1):

[

4 – (-10) = 4 + 10 = 14

]

3. Substitute these into the distance formula:

[

d = sqrt{(7)^2 + (14)^2}

]

[

d = sqrt{49 + 196}

]

[

d = sqrt{245}

]

[

d approx 15.65

]

So, the distance between the two points is approximately 15.65.

To find the distance between the points ((-5, -10)) and ((2, 4)), we can use the distance formula:

[

d = sqrt{(x_2 – x_1)^2 + (y_2 – y_1)^2}

]

Where ((x_1, y_1)) and ((x_2, y_2)) are the coordinates of the two points.

1. Here, ((x_1, y_1) = (-5, -10)) and ((x_2, y_2) = (2, 4)).
2. Calculate the differences:

– (x_2 – x_1 = 2 – (-5) = 2 + 5 = 7)

– (y_2 – y_1 = 4 – (-10) = 4 + 10 = 14)

3. Now plug these values into the formula:

[

d = sqrt{(7)^2 + (14)^2} = sqrt{49 + 196} = sqrt{245}

]

4. Finally, simplify (sqrt{245}):

[

sqrt{245} = sqrt{49 times 5} = 7sqrt{5} approx 15.65

]

Therefore, the distance between the points