Question

Find the distance between the points (–9, 0) and (2, 5).

Answer 1

The distance between the points (–9, 0) and (2, 5) in the Cartesian plane is approximately
`√(146)` units.

Step-by-step explanation:

To find the distance between two points in the Cartesian plane, we can use the distance formula.

The distance formula is:

distance =
`√(((x_2 - x_1)^2 + (y_2 - y_1)^2))`

Using the given points (–9, 0) and (2, 5), we can plug in the values:

distance =
`√(((2 - (-9))^2 + (5 - 0)^2))`

distance =
`√(((11)^2 + (5)^2))`

distance =
`√((121 + 25))`

distance =
`√(146)`

So, the distance between the points (–9, 0) and (2, 5) is approximately
`√(146)` units.

Answer 2

sqrt( 146)

Step-by-step explanation:

To find the distance between two points, we use the formula

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

Where (x1,y1) and (x2,y2) are the two points.

(–9, 0) and (2, 5).

Substituting into the equation

d = sqrt( (5-0)^2 + (2- -9)^2)

d = sqrt( ( 5^2 + (2+9)^2)

sqrt( ( 5^2 + (11)^2)

= sqrt( 25+121)

= sqrt( 146)

The distance between the two points is sqrt(74)