Question

Which expression gives the distance between the points (4, 6) and (7, -3)?

Answer 1

The distance formula is

`√((x_2-x_1)^2+(y_2-y_1)^2)`. In the ordered pair (4, 6), 4 is the x-coordinate and 6 is the y-coordinate. In the ordered pair (7, -3), 7 is the x-coordinate and -3 is the y-coordinate. Substituting those values in gives us

`√((4-7)^2+(6--3)^2)`. Since subtracting a negative is the same as adding a positive, we now have

Answer 2

The expression gives the distance between the points (4, 6) and (7, -3) is Option (C) .

i.e

`Distance\ formula = \sqrt{(7 - 4)^(2) + (6 +3)^(2)}`

Explanation:

Formula

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

As the point are (4, 6) and (7, -3) .

Put points in the formula

`Distance\ formula = \sqrt{(4 -7)^(2) + (6- (-3))^(2)}`

`Distance\ formula = \sqrt{(7 - 4)^(2) + (6 +3)^(2)}`

`Distance\ formula = \sqrt{(3)^(2) + (9)^(2)}`

`Distance\ formula = √(9 + 81)`

`Distance\ formula = √(90)`

`√(90) = 9.5\ units\ (Approx)`

Distance formula = 9.5 Units (Approx)

Therefore Option (C) is correct.