My Attempt Thus far.. I tried using the quadratic formula on this to find the distance/magnitude , however it did not work. I then tried to solve it as a quadratic inequality. Can anyone help? And please I would like to know how the answer can be achieved really step by step.
The distance from point (−1, 1) to (2, −) is 5/13 of the distance from (14, 2) to (2, −). If it is known that > 0, find .
On
Since you said you used the quadratic formula, perhaps you made a math error. As the comment says, please show more of your work. You can learn mathjax here which is similar to latex.
Here is the worked out answer.
$$ \sqrt{(2-(-1))^2 + (-s-1)^2} = \frac{5}{13} \sqrt{(2-14)^2 + (-s-2)^2} $$ $$ \sqrt{9 + s^2+2s+1} = \frac{5}{13} \sqrt{144 + s^2+4s+4} $$ $$ \sqrt{s^2+2s+10} = \frac{5}{13} \sqrt{s^2+4s+148} $$
$$ s^2+2s+10 = \frac{25}{169} \cdot \left(s^2+4s+148\right) $$
$$ 169s^2 + 338s + 1690 = 25s^2 + 100s + 3700 $$
$$ 144s^2 + 238s - 2010 =0 $$
$$ 72s^2 + 119s - 1005 =0 $$
Quadratic formula:
$$ \frac{-119 \pm \sqrt{119^2-4\cdot72 \cdot (-1005)}}{144}$$
$$ \frac{-119 \pm 551}{144} $$
We want only the positive $s$ so:
$$ \frac{432}{144} $$
$$ s=3 $$
Step 1: compute the square of the first distance, a quadratic polynomial in
s.Step 2: compute the square of the second distance, a quadratic polynomial in
s.Step 3: express that the first squared distance is the second squared distance times a known constant.
Step 4: move all terms to the same member.
Step 5: solve the quadratic equation.
Step 6: discard the negative solution.