Find the points

Question

1.  Consider the points   P= (-3,2)  and Q = (2,1).

a.  find the slope of the line through P and Q.

b.  find the equation of the line passing through P and Q.

c.  Find the distance between P and Q.

 

 

2.  Find the point of intersection for the lines y= x + 1  and y = -2x + 4.

 

 

 

Answer 1

1.  P= (-3,2)   Q=(2,1)

 

a.  slope = rise/run= (y₂-y₁)/(x₂-x₁)

     m = (1-2)/(2-(-3))=-1/5

 

b.  For the equation we can use point slope form

     y-y₁ = m(x-x₁). Let's use point P (-3,2)

     y-2=-1/5(x-(-3))

     5y-10=-(x+3)

     5y-10=-x-3

     x+5y=7

 

c.  distance = √((x₂-x₁)²+(y₂-y₁)²) 

     =√((-3-2)²+(2-1)²) 

     = √26

 

2.  intersection of  

     y=x+1

     y=-2x+4

 

Substitute x+1 for y in eqn 2

 

x+1=-2x+4

3x+1=4

3x=3

x=1

 

y=x+1=2

 

The lines intersect ar the point (1,2)