The endpoints of ab are a(1, 4) and b(6, -1). if point c divides ab in the ratio 2:3, what would the coordinates of C be? If point d divides ab in the ratio 3:2, what would the coordinates of D be?

C (3,2) D (4,1)

Step-by-step explanation:

The x distance is 5 and y distance is 5.

Point C will cause ac:bc to be 2:3. Add 2 to the x value and subtract 2 to the y value in a to get point c.

Point D will cause ad:bd to be 3:2. Add 3 to the x value and subtract 3 to the y value in a to get point d.

The reason why you subtract for the y value is because the y value from a to b decreases.

10010010001010010101001001010010100101010010101010010010101010110010001011010010010001

step-by-step explanation:

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240