So, I've spent hours on this question and it's frustrating me way too much so I created an account for StackExchange just to understand how you solve this problem.
Let me start by sharing the question: "Sally has hidden her brother's birthday present somewhere in the backyard. When writing instructions for finding the present, she used a coordinate system with each unit on the grid representing 1 m. The positive y-axis of this grid points north. The instructions read "Start at the origin, walk halfway to (8,6), turn 90 degrees left, and then walk twice as far." Where is the present?" By the way, you have to answer the question algebraically and the answer in the textbook is (-2,11)
What I Know
Let P represent the coordinate of the present
Let M represent the midpoint between (0,0) and (8,6)
- M is at (4,3) which is solved using the midpoint formula.
- The distance from P to M is 10 m.
- The equation for the line from the origin to the midpoint is:
y= $\frac{3x}{4}$ - The equation for line PM is:
y= $\frac{-4x}{3}$ + $\frac{25}{3}$ - Using the distance formula for two coordinates I know that the distance from M to P can be represented in this equation: $100=(4-x)^2 + (3-y)^2$ The x and y in the equation represents the x,y coordinates of the point P. I don't know how to simplify this equation further.
My troubles
I come to this point where I don't know what to do anymore. Please explain how you solved this problem.
Thank you so much
Best Answer
Equivalent to 4 steps east, 3 steps north, then 8 steps north, 6 steps west, resulting in (4-6, 3+8) or (-2, 11). After plotting, it's much easier to see the triangles you have to describe algebraically.