P (2, 3) and Q (6, 10) are two points on the Cartesian plane.
Find the length of PQ
Find the coordinates of the midpoint of PQ
Find the equation of PQ

Step-by-step explanation:

Given:

Let S be the mid-point of PQ.

Equation of line PQ is given as:

length = square root of ((2-6)^2)+((3-10)^2) = square root (of) 16+49

square root of 65 =  8.062257748  = approx 8.1

midpoint = (x1+x2)/2  ,  (y1+y2)/2

= 2+6  /2  ,  3+10  /2

=8/2 , 13/2

= 4, 6.5 (midpoint)

equation= y=mx+c

m(gradient) = (y2-y1)/(x2-x1) or (y1-y2)/(x1-x2)

= so,  (3-10)/(2-6)  (y1-y2)/(x1-x2)- i normally use this one

= -7/-4 = 1.75

so y=1.75x+c

plug in the values from any one of them (2,3) or (6,10)

to get

for example:  3=1.75*2+c

3=3.5+c

-0.5=c

now we get the equation y=1.75x+(-0.5)

you always have to have a plus( +(-0.5)) since the equation is y=mx+c

the image of (6, 9) under a dilation is (4, 6). the scale factor is

because linear equations are a lot simpler than quadratics equations, and linear equations formula is a lot easier to memorize. that's why i think they're harder.