What set of reflections and rotations would carry rectangle ABCD onto itself?

A. Rotate 180°, reflect over the y-axis, reflect over the line y-x
B. Reflect over the y-axis, rotate 180°, reflect over the x-axis
C. Rotate 180°, reflect over the y-axis, reflect over the line y=x
D. Reflect over the y-axis, reflect over the x-axis, rotate 180°

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step-by-step explanation:

graph b

step-by-step explanation:

one solution- graph a (clear intercepting point.)

no solution- graph b (they're parallel, there will never be a point of interception.)

infinite solutions- graph c (all points intercept.)

x coordinate can be written by using the formula, x= x1 + 2/5(x2 - x1)

step-by-step explanation:

formula

x = x1 + p/w(x2 - x1)

let the line segment ab with a(x1,y1) and b(x2,y2)

a point(x,y) divide ab in the ratio, 2: 3 the x coordinate can be written as

x = x1 + p/w(x2 - x1)

here p=2 and w = 2+3

therefore,

x coordinate can be written by using the formula, x= x1 + 2/5(x2 - x1)

similarly y coordinate y = y1 + 2/5(y2 - y1)