Triangle xyz is located at x (-2, 1), y (-4, -3), and z (0, -2). the triangle is then transformed using the rule (x-1, y+3) to form the image x'y'z'. what are the new coordinates of x', y', and z'? describe what characteristics you would find if the corresponding vertices were connected with line segments.

Step-by-step explanation:

The coordinates of the image points are found by adding (-1, 3) to the coordinates of the original points, as the transformation rule tells you. Then ...

... X' = X + (-1, 3) = (-2-1, 1+3) = (-3, 4)

... Y' = Y + (-1, 3) = (-4-1, -3+3) = (-5, 0)

... Z' = Z + (-1, 3) = (0-1, -2+3) = (-1, 1)

Since each image point is 1 unit to the left and 3 units up from its original, the line segment connecting them will be joining two points that are separated by 1 horizontal unit and 3 vertical units. The line segments will all be parallel (with slope -3) and of the same length (√(1²+3²) = √10).

the answer is 489

step-by-step explanation:

hello from mrbilldoesmath!

answer:

(7 x + 6 y) (49 x^2 - 42 x y + 36 y^2)

discussion:

the trick is to recognize that 343 = 7^3 and 216 = 6^3 and, in general,

a^3 + b^3 =   (a + b) (a^2 - a b + b^2).

in our case

343x^3+216y^3   =   (7x)^3 + (6y)^3

so take a = 7x and b = 6y in the above equation to get the answer.

you,

mrb