Line segment ab is given by the coordinates a (-4, 16) and b (-4, 32). find the two sets of coordinates that could partition this segment in the ratio 3: 1 or 1: 3.

The required sets of coordinates are (-4,28) and (-4,20).

Step-by-step explanation:

Given information: A (-4, 16) and B (-4, 32).

Section formula:

If end point of a line segment are and and a point divides that line segment in m:n, then the coordinates of that point are

If a point divides AB in 3:1, then coordinates of that point are

If a point divides AB in 1:3, then coordinates of that point are

Therefore the required sets of coordinates are (-4,28) and (-4,20).

34.5 cm

step-by-step explanation:

generally for a circular segment of angle, θ° and radius r

arc length

= (θ/360) x circumference

= (θ/360) x 2πr

in our case, θ = 60°, π=3.142 and r = 33 cm

substitute into above formula

arc length

= (60/360) x 2(3.142)( 33) = 34.5 cm