To find the distance between two points with known coordinates, we can use the Distance Formula. Let A( x_1, y_1) and B( x_2, y_2) be two points in the coordinate plane. Then, the distance between these two points AB can be calculated as follows.
AB=sqrt(( x_2- x_1)^2+( y_2- y_1)^2)
Now, we are asked to calculate the distance between points A(13,2) and B(7,10). Let's substitute the coordinates of these points into the Distance Formula.
Now, the difference between the x-coordinates of the points is the length of one of the legs of the triangle. The length of the other leg is the difference between the y-coordinates. Therefore, the lengths of the legs are x_2-x_1 and y_2-y_1. Let's write the equation for this triangle based on the Pythagorean Theorem. AB^2=( x_2-x_1)^2+( y_2-y_1)^2 ⇕
AB=sqrt((x_2-x_1)^2+(y_2-y_1)^2)
Notice that, when solving for AB, we only need to consider the principal root because AB must be positive.
