Given the points R(-4, 5) and S(2, -1). Find RS, the midpoint of RS, and point P which is 13 of the distance from R to S. Leave your answer as a simplified radical.

Step-by-step explanation:

Given the points R(-4, 5) and S(2, -1), to get the distance between the points, we will use the formula;

D = √(x2-x1)²+(y2-y1)²

Given x1= -4, y1 = 5, x2 = 2 and y2 = -1

RS = √(2-(-4))²+(-1-5)²

RS = √(6)²+(-6)²

RS = √36+36

RS = √72

RS = √2×36

RS = 6√2units

To get the midpoint, we will use the formula M(X,Y) = (x1+x2/2, y1+y2/2)

(X,Y) = (-4+2/2, -1+5/2)

(X,Y) = (-2/2, 4/2)

(X,Y) = (-1,2)

Hence the midpoint is (-1,2)

To get a point P 1/3 of the distance of RS, we will multiply 1/3 with the the distance RS as shown

P = 1/3 × 6√2

P = 2√2

y = 5x + 17

step-by-step explanation:

a perpendicular line will be the opposite reciprocal slope of the given equation.   the slope given is -1/5 so the opposite reciprocal is 5

find b:

7 = 5 (-2) + b

7 = -10 + b

17 = b

write equation

y = 5x + 17