Question

Laura says that the distance between (4, -2) and (4, -7) in the coordiante plane is equal to |-2 - (-7)| units. Ryan says that the distance between the points (2,3) and (-9, 3) in the coordinate plane is equla to |2 +9| units.Is either Laura or Ryan correct? (Write Laura, Ryan, Both, or Neither) Explain.

Answer 1

Laura is correct and Ryan is incorrect. The distances between the given points are 5 units and 11 units, respectively.

Step-by-step explanation:

Laura is correct. To find the distance between two points in the coordinate plane, you can use the distance formula. The distance formula is d = √((x2 - x1)^2 + (y2 - y1)^2), where (x1, y1) and (x2, y2) are the coordinates of the two points.

For Laura's example, the distance between (4, -2) and (4, -7) is equal to

√((4 - 4)^2 + (-2 - (-7))^2) = √((0)^2 + (5)^2) = √(0 + 25) = √25 = 5 units.

For Ryan's example, the distance between (2, 3) and (-9, 3) is equal to

√((2 - (-9))^2 + (3 - 3)^2) = √((11)^2 + (0)^2) = √(121 + 0) = √121 = 11 units.

Therefore, Laura is correct and Ryan is incorrect. The distances between the given points are 5 units and 11 units, respectively.