Question

Drag the tiles to the correct box?

Answer 1

1. (3,-1) and (5,4)

`Distance\ = 5.39`

2. (2,3) and (4,5)

`Distance\ = 2.83`

3. (-5,7) and (8,5)

`Distance = 13.15`

4. (-2,4) and (3,-1)

`Distance = 7.07`

Explanation:

Given

The attached

Required

Calculate the distance between each points;

Distance between points is calculated using;

`d =√((x_1 - x_2)^2 + (y_1 - y_2)^2)`

1. (3,-1) and (5,4)

Here;
`x_1 = 3; x_2 = 5; y_1 = -1; y_2 = 4`

Substitute these values in the formula above

`d =√((3 - 5)^2 + (-1 - 4)^2)`

`d =√(- 2^2 + (-5^2))`

`d =√(4 + 25)`

`d =√(29)`

`d = 5.39` (Approximated)

2. (2,3) and (4,5)

Here;
`x_1 = 2; x_2 = 4; y_1 = 3; y_2 = 5`

Substitute these values in the formula above

`d =√((2 - 4)^2 + (3 - 5)^2)`

`d =√(- 2^2 + (-2^2))`

`d =√(4 + 4)`

`d =√(8)`

`d = 2.83` (Approximated)

3. (-5,7) and (8,5)

Here;
`x_1 = -5; x_2 = 8; y_1 = 7; y_2 = 5`

Substitute these values in the formula above

`d =√((-5 - 8)^2 + (7 - 5)^2)`

`d =√(- 13^2 + 2^2)`

`d =√(169 + 4)`

`d =√(173)`

`d = 13.15` (Approximated)

4. (-2,4) and (3,-1)

Here;
`x_1 = -2; x_2 = 3; y_1 = 4; y_2 = -1`

Substitute these values in the formula above

`d =√((-2 - 3)^2 + (4 - (-1))^2)`

`d =√(- 5^2 + (4+1)^2)`

`d =√(- 5^2 + 5^2)`

`d =√(25 + 25)`

`d =√(50)`

`d = 7.07` (Approximated)