Question

Use the distance formula to find the distance between the points (-8, -7)(−8,−7) and (-1, -8)(−1,−8). (Write your answer in exact form.)

A)√50
​

B)√51
​

C)√52

D)√53
​

Answer 1

A)
`√(50)`

Step-by-step explanation:

1. Know that the distance formula is
`d=√((x_2-x_1)^2+(y_2-y_1)^2)`.

2. Identify the values for each variable; coordinates are written in the form
`(x,y)`.

• For the purpose of this explanation, let's make
  `(x_1, y_1)=(-8,-7)` and
  `(x_2, y_2)=(-1,-8)`.

3. Now that you have identified the values for each variable, plug them into the distance formula equation.

• 
  `d=√((-1-(-8))^2+(-8-(-7))^2)`
• When plugging in points, make sure you're plugging in the correct values; be sure that values of the same coordinate have the same subscript.

4. Solve for the equation.

• Cancel out the negatives:
  `d=√((-1+8)^2+(-8+7)^2)`
• Add:
  `d=√((7)^2+(-1)^2)`
• Apply the exponents:
  `d=√(49+1)`
• Add:
  `d=√(50)`

5. The distance between the two points is
`√(50)`.

Answer 2

The distance between the points (-8, -7) and (-1, -8) is sqrt(50).

Step-by-step explanation:

To find the distance between the points (-8, -7) and (-1, -8), we use the distance formula:

d = sqrt((x2 - x1)^2 + (y2 - y1)^2)

Substituting the values, we get:

d = sqrt((-1 - (-8))^2 + (-8 - (-7))^2)

= sqrt((7)^2 + (-1)^2) = sqrt(49 + 1) = sqrt(50)

So, the distance between the points is sqrt(50), which is answer choice A.