What is the distance between #(-5,2 ) # and # (4, 7) #?

# sqrt 106 # ≈ 10.3 (1 decimal place )

Explanation:

To find the distance (d ) between 2 coordinate points # (x_1 , y_1 ) and ( x_2 , y_2 ) #

Use the distance formula which is given as

# color(red)( d = sqrt ((x_2 - x_1 )^2 + ( y_2 - y_1 )^2 #

For the coordinate pairs given let # ( -5 , 2 ) = ( x_1 , y_1 ) , (4 , 7) = ( x_2 , y_2 ) #

substituting into the formula

# d = sqrt (4 - (-5)^2 + (7 - 2 )^2 #

# = sqrt( 9^2 + 5^2 #

=# sqrt ( 81 + 25) = sqrt 106 # ≈ 10.3 (1 decimal place )