Question

1. mathematical connections tao rides his bike in a straight line from his location, perpendicular to path a, and luke rides his bike in a straight line from his location, perpendicular to path b. what are the coordinates of the point where they meet?

Explanation:

Step1: Identify the starting - point coordinates

Assume Tao's starting - point is \((x_1,y_1)\) and from the graph, it seems Tao is at \((1,2)\) and Luke's starting - point is \((x_2,y_2)=(9,8)\). Path A and Path B are not given explicitly, but since Tao rides perpendicular to path A and Luke rides perpendicular to path B, we assume they are moving towards the intersection along the shortest perpendicular lines.

Step2: Find the mid - point formula

The point where they meet is the mid - point of the line segment connecting their starting points. The mid - point formula between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \((\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})\).

Step3: Substitute the values

Substitute \(x_1 = 1,y_1=2,x_2 = 9,y_2 = 8\) into the mid - point formula.
\[x=\frac{1 + 9}{2}=\frac{10}{2}=5\]
\[y=\frac{2+8}{2}=\frac{10}{2}=5\]

Answer:

\((5,5)\)