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

Answer:

10 units

Option C is the correct option

Step-by-step 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

$= \sqrt{36 + 64}$

Add the numbers

$= \sqrt{100}$

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..

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