Question

What is the distance between (3, 5.25) and (3, –8.75)? 6 units 8.25 units 11.75 units 14 units

Answer 1

By using distance formula :



`\text{Distance formula,} \bold{ \boxed{ Distance = \sqrt{( x_(2) -x_(1))^(2)+(y_(2) - y_(1))^(2)) }}}`





Given points = ( 3 , 5.25 ) and ( 3 , - 8.75 )



`\bold{Taking \: \: \: x_(1)=3 \: \: , \: \: x_(2)= 3 \: \: , \: \: y_(1)= 5.25 \: \: , \: \: y_(2)= -8.75}`




On applying formula, we get



`Distance = \sqrt{ ( x_(2)-x_(1))^(2)+(y_(2)-y_(1))^2} \\ \\ \\ Distance = \sqrt{ ( 3 - 3 )^(2) + ( - 8.75 - 5.25 )^(2)} \\ \\ \\ Distance = \sqrt{ ( 0 )^(2) + ( - 14)^(2)} \\ \\ \\ Distance = \sqrt{ ( - 14 )^(2)} \\ \\ \\ Distance = \sqrt{ 14^(2)} \:\:\:\:\:\:\:\:\:\:\: \: \: \: \: \: \: \: \: | \bold{ ( - 14 )^(2) = 14^(2)} \\ \\ \\ Distance = {14}^{2 * (1)/(2) } \\ \\ \\ Distance = {14}^(1) \\ \\ \\ Distance = 14 \: units`








Hence, Option D is correct.

Answer 2

D. 14 units.

Explanation:

We have been given coordinates of two points. We are asked to find the distance between both points.

We will distance formula to solve our given problem.

`D=√((x_2-x_1)^2+(y_2-y_1)^2)`, where,

`x_2-x_1` = Difference between two x-coordinates,

`y_2-y_1` = Difference between two y-coordinates of same x-coordinates,

Let
`(3,5.25)=(x_1,y_1)` and
`(3,-8.75)=(x_2,y_2)`.

Upon substituting our given values in above formula, we will get:

`D=√((3-3)^2+(-8.75-5.25)^2)`

`D=√((0)^2+(-14)^2)`

`D=√(0+196)`

`D=√(196)`

`D=14`

Therefore, the distance between the given points is 14 units and option D is the correct choice.