Line k contains points A, B, C, and D. EA represents the difference between the y-coordinates and EC represents the difference between the x-coordinates of points A and C. Likewise, FB represents the difference between the y-coordinates and FD represents the difference between the x-coordinates of points B and D. Use similar triangles to explain why the slope of like k is the same whether the slope is calculated using points A and C or points B and D.

Brittany has designed four different birdcages, each with the same volume: a square pyramid, a cylinder, a cone, and a sphere. the zoo wants to use one of brittany’s designs but plans to change the volume of the cage. find the design change that would result in the birdcage with the greatest volume. a.) increase the area of the base of the square pyramid by a factor of ten. b.) increase the height of the cylinder by a factor of ten. c.) increase the radius of the cone by a factor of ten. d.) increase the radius of a sphere by a factor of ten.