Translate abc by (4,4), rotate 90 degrees counterclockwise around a, and reflect over the y-axis. points: a(-1,2) b(-3,4) c(-2,5)pease !

Given A(-1,2) , B(-3,4) and C(-2,5) are the vertices of a triangle.

Let us find new coordinates after translating by (4,4)

New coordinates are A(-1+4,2+4), B(-3+4,4+4) and C(-2+4,5+4)

                                 = A(3,6),B(1,8) and C(2,9)

Now it is rotated counterclockwise around A(3,6). That means A remains same and we need to find new coordinates of B and C.  To find B and C let us make origin as A and find B ,C coordinates from it.

B'= (1-3,8-6) = (-2,2)

C'=(2-3,9-6)=(-1,3)

Now B' anc C' are rotated 90 degrees counter clockwise about origin. Hence (x,y) becomes (-y,x).

Hence B'(-2,2) becomes (-2,-2) and C'(-1,3) becomes (-3,-1).

Now let us move origin from (3,6) to (0,0) again.

Hence new coordinates of B are (-2+3,-2+6) = (1,4)

And new coordinates of C are (-3+3,-1+6) = (0,5)

Coordinates of triangle till translation and rotation are A(3,6) B(1,4) and C(0,5).

Now it is reflected over x-axis which means x-coordinate changes its sign.

Hence new coordinates of triangle after reflection over x-axis = A(-3,6),B(-1,4) and C(0,5)

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step-by-step explanation:

answer: (c) m∠qpo + (2x + 16)° = 180°

step-by-step explanation:

the opposite angles of a quadrilateral are supplementary.

so, ∠o + ∠q = 180°   and   ∠p + ∠r = 180°

since ∠r = 2x + 16°, we can use substitution as follows:

∠p + ∠r = 180°

∠p + (2x + 16)° = 180°