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The coordinates of the top of a tree are -3,8 , and an acorn is attached to the tree at -1,5 If we know that the acorn lies exactly halfway between a squirrel and the top of the tree, what are the coordinates of the squirrel?

Thanx!!!!!!!!!!!!!!!!!!!!!!

Jul 9, 2022

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What are the coordinates of the squirrel?

Hello Guest!

$$P_1(-3,8)\\ P_2(-1,5)\\ m=\frac{y_2-y_1}{x_2-x_1}=\frac{5-8}{-1-(-3)}\\ \color{blue}m=-1.5$$

$$y=m(x-x_1)+y_1\\ y=-1.5(x-(-3))+8=-1.5x-4.5+8\\ \color{blue}y=-1.5\cdot x+3.5\\ y_3=y_2-(y_1-y_2)\\ y_3=5-(8-5)\\ \color{blue}y_3=2$$

$$y_3=-1.5\cdot x_3+3.5\\x_3=\frac{y_3-3.5}{-1.5}=\frac{2-3.5}{-1.5}\\ \color{blue}x_3=1\\ \color{blue}The\ coordinates\ of\ the\ squirrel\ are\ 1,2.$$

!

Jul 9, 2022
edited by asinus  Jul 9, 2022