Monoxdifly
MHB
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The point A is located on the coordinate (0, 5) and B is located on (10, 0). Point P(x, 0) is located on the line segment OB with O(0, 0). The coordinate of P so that the length AP + PB minimum is ...
A. (3, 0)
B. (3 1/4, 0)
C. (3 3/4, 0)
D. (4 1/2, 0)
E. (5, 0)
What I did:
f(x) = AP + PB =$$\sqrt{5^2+x^2}+(10-x)=\sqrt{25+x^2}+10-x$$
In order to make AP + PB minimum, so:
f'(x) = 0
$$\frac12(25+x^2)^{-\frac12}(2x)+(-1)=0$$
$$\frac{x}{\sqrt{25+x^2}}=1$$
$$x=\sqrt{25+x^2}$$
$$x^2=25+x^2$$
This is where I got stuck. Subtracting $$x^2$$ from both sides would leave me with 0 = 25 which is obviously incorrect. Where did I do wrong?
A. (3, 0)
B. (3 1/4, 0)
C. (3 3/4, 0)
D. (4 1/2, 0)
E. (5, 0)
What I did:
f(x) = AP + PB =$$\sqrt{5^2+x^2}+(10-x)=\sqrt{25+x^2}+10-x$$
In order to make AP + PB minimum, so:
f'(x) = 0
$$\frac12(25+x^2)^{-\frac12}(2x)+(-1)=0$$
$$\frac{x}{\sqrt{25+x^2}}=1$$
$$x=\sqrt{25+x^2}$$
$$x^2=25+x^2$$
This is where I got stuck. Subtracting $$x^2$$ from both sides would leave me with 0 = 25 which is obviously incorrect. Where did I do wrong?