The smaller triangle is the image of the larger triangle after a dilation. the center of the dilation is (4,2). what is the scale factor used to create the dilation?

Small triangle: The side // x axis has a length of 4
Large triangle: The side // x axis has a length of 12

So Small/Large = 4/12 = 1/3

Small triangle: The side // y axis has a length of 3
Large triangle: The side // y axis has a length of 9

So Small/Large = 3/9 = 1/3

So the scale factor to obtain this dilatation is 1/3

c) 6

step-by-step explanation:

let pq = qr = rs = x, and xz = y and zu = z.

if the horizontal lines are parallel, then corresponding segments are in proportion:

substitute:

therefore 3 = y = z.

xu = y + z → xu = 3 + 3 = 6

Ok here we go ..there are plenty of ways to solve such math problems but we will go for the smartest and easiest ..5x+2y=7  -2x+6y=9we rearrange them into the following ..by multiplying the 1st equation by 2 it becomes 10x + 4y = 14we rearrange it and so it becomes 10x = 14 - 4yas for the second equation we multiply it by 5 and rearrange it so it becomes as to the following ..-10x + 30y = 45rearranging so 10x = 30y -45now 10x equals both 14 - 4y and 30y -45so   14 - 4y = 30y -4531 = 26yy= 31/26 = 1.19 or around 1.2so by now we can calculate x easily as  -2x+6y=9so 2x = 6y -9 = 6 * 31/26 - 9 = -1.84  then x = - 0.92 or around -0.9best luck!