Question

Consider the line y=10 x -1 and the point P=(2,0). (a) Write the formula for a function d(x) that describes the distance between the point P and a point (x,y) on the line. You final answer should only involve the variable x. Then d(x) =

Answer 1

Answer:

the formula for a function d(x) that describes the distance is $d(x)=\sqrt{101x^{2}-24x+5}$

Step-by-step explanation:

We are going to define final point $P_{f}=(2,0)$, and initial point $P_{i}=(x,y)=(x,10x-1)$, then we can use $d=\sqrt{(x_{f}-x_{i})^{2}+(y_{f}-y_{i})^{2}}$, so we obtain $d(x)=\sqrt{(2-x)^{2}+(0-(10x-1))^{2}}$, by developing it $d(x)=\sqrt{(2-x)^{2}+(0-(10x-1))^{2}}\\d(x)=\sqrt{4-4x+x^{2}+(1-10x)^{2}}\\d(x)=\sqrt{4-4x+x^{2}+1-20x+100x^{2}}\\d(x)=\sqrt{101x^{2}-24x+5}$

This formula describes the distance between those two points and involves x