Question

a point is reflected in the x-axis the new point is (5, -3.5) what is the distance between the two points? Urgent pls help

Answer 1

Distance between two points is 7

Step-by-step explanation:

This is a question based on reflection of point w.r.t line. During reflection we can see the mirror image with t-shirt print inverted.But the distance from mirror remains same.

Assume a point (x,y), and it reflect in x-axis, then x-axis serves as the mirror, and the new point is (x,-y), because the distance from the mirror remains same. If the reflection of the point is (x,y) in y-axis, then y-axis serves as the mirror, and the new point is (-x,y). And if you reflect (x,y) in y=x line, then new point will be (y,x).

So considering the above question, if new point is (5, -3.5), then the original point must be (5, 3.5)

Distance between two points
`P(X_1, Y_1)` and
`Q(X_2, Y_2)`is given by:

d(P, Q) =
`\sqrt{ (X_2-X_1)^(2) + (Y_2-Y_1)^(2)}`

`Y_2-Y_2 = (3.5) - (-3.5) = 3.5+3.5 = 7\\ \\X_2-X_1 = 5 - 5 = 0`

`So \sqrt {(Y_2-Y_1)^(2) + (X_2-X_1)^(2)} = \sqrt { 7^(2) + 0^(2)} = \sqrt { 14+0} = \sqrt {14} = 7`

So distance = 7