The slope of a line through A(-1, 1) is 3. Locate the point on this line that is 2 square root of 10 from A.

Question

I have no idea how to solve this, can you please help me?

Answer 1

Let the point be (x,y). then we have 2 equations (slope and distance) from point A. 

The slope in point slope form is

y-1=3(x- -1) or 

y-1=3x+3 Or 

y=3x+4

 

the distance equation 

 

2 sqrt(10)= sqrt [(x- -1)²+(y-1)²]

squaring both sides 

4(10)=(x+1)²+(y-1)²

substitute the top equation in for y and simplify 

40=x² +2x+1+(3x+3)²

40=x²+2x+1+9x²+18x+9

40=10x²+20x+10

divide both sides by 10 and move everything to one side of equation

0=x²+2x-3

factor

0=(x+3)(x-1)

x=1,-3

substitute back in to find y

y=3(1)+4=7

y=3(-3)+4=-5

So there are 2 points on the line that satisfy these conditions (check is left to you)

(1,7) and (-3,-5)