Question

A mother fox is watching her kit play in a meadow. Assume the meadow is mapped onto the coordinate plane as shown in the graph. What is the exact distance from the mother fox to her kit? (I prefer the answer to be in square root form.)

Answer 1

Hello there. To solve this question, we have to remember how to determine the distance between two points in the coordinate plane.

Given two points A = (x0, y0) and B = (x1, y1) in a coordinate plane, using the Pythagoras theorem, is easy to determine that the distance d(A, B) is given by the following expression:

`d(A,\,B)=√((x_1-x_0)^2+(y_1-y_0)^2)`

In this case, the points are the coordinates of the mother fox and her kit, given by

`A=(-7,\,7)\text{ and }B=(7,\,2)`

Using the formula, we get

`d(A,\,B)=√((7-(-7))^2+(2-7)^2)`

Adding the values inside parenthesis, we get

`d(A,\,B)=√(14^2+(-5)^2)`

Square and add the numbers

`d(A,\,B)=√(196+25)=√(221)`

This is the distance between the mother fox and her kit.