Question

what is the distance between the points (4, 5) and (10, 13) on a coordinte plane a. 12 units b. 8 units c. 10 units d. 14 units

Answer 1

10 units

Option C is the correct option

Explanation:

Let the points be A and B

A ( 4 , 5 ) ------> ( x1 , y1 )

B ( 10 , 13 ) ------> ( x2 , y2 )

Now, let's find the distance between these points:

`\sqrt{ {(x2 - x1)}^(2) + {(y2 - y1)}^(2) }`

plug the values

`= \: \sqrt{(10 - 4) ^(2) + {(13 - 5)}^(2) }`

Calculate the difference

`= \sqrt{ {(6)}^(2) + {(8)}^(2) }`

Evaluate the power

`= √(36 + 64)`

Add the numbers

`= √(100)`

Write the number in exponential form with. base of 10

`= \sqrt{ {(10)}^(2) }`

Reduce the index of the radical and exponent with 2

`= 10 \: units`

Hope this helps..

Best regards!!