Question

After drawing the line y = 2x − 1 and marking the point A = (−2, 7), Kendall is trying to decide which point on the line is closest to A. The point P = (3, 5) looks promising. To check that P really is the point on y = 2x − 1 that is closest to A, what should Kendall do? Is P closest to A?

Answer 1

Answer:

Step-by-step explanation:

Having drawn the line, Kendall must verify that the point P belongs to the line y = 2x-1 and then calculate the distance between A-P  and verify if it is the closest to A or there is another one of the line

Having the point P(3,5) substitue x to verify y

y=2*(3)-1=6-1=5 (3,5)

Now if the angle formed by A and P is 90º it means that it is the closest point, otherwise that point must be found

$d_{AP}=\sqrt{(y_{2}-y_{1})^{2}+(x_{2}-x_{1})^{2}}=\sqrt{(5-7)^{2}+(3-(-2}))^{2}}=\\\sqrt{(-2)^{2}+(5)^{2}}=\sqrt{29}$

and we found the distance PQ and QA

; $d_{PQ}=\sqrt{125}$, $d_{QA}=12$

be the APQ triangle we must find <APQ through the cosine law (graph 2).