PLEASE HURRY perform the following series of rigid transformations on ∆abc
translate triangle abc by moving it 5 units to the right and 2 units up
Draw the line y=-x and reflect Triangle A’B’C’ across the line
Rotate A’’B’’C’’ counterclockwise about the fact origin by 270 degress

Step-by-step explanation:

Coordinates of the vertices of ΔABC,

A(-6, -1), B(-3, -3), C(-1, -2)

Step - 1

Rule for the translation of a point (x, y) by 'h' units right and 'k' units upwards,

A(x, y) → A(x + h, y + k)

If ΔABC is translated by 5 units right and 2 units up, image points will be,

A(-6, -1) → H(-6 + 5, -1 + 2)

            → H(-1, 1)

B(-3, -3) → J(-3 + 5, -3 + 2)

             → J(2, -1)  

C(-1, -2) → K(-1 + 5, -2 + 2)

            → K(4, 0)

Step - 2

If the image triangle HJK is reflected across a line , rule for the reflection will be,

H(x, y) → A'(-y, -x)

By this rule,

H(-1, 1) → A'(-1, 1)

J(2, -1) → B'(1, -2)

K(4, 0) → C'(0, -4)

Step - 3

Rule for the rotation of a point 270° counterclockwise about the origin,

A'(x, y) → A"(y, -x)

By this rule, image points of ΔA'B'C' will be,

A'(-1, 1) → A"(1, 1)

B'(1, -2) → B"(-2, -1)

C'(0, -4) → C"(-4, 0)

Now we can graph the image triangle A"B"C".

(∠ABC) 108 (for all)

(∠ACB) 27 (for all)

(∠CAB) 45 (for all)

Step-by-step explanation:

step-by-step explanation :

we know that

the measurement of the outer angle is the semi-difference of the arcs which comprises

in this problem

m< xzy is the outer angle

substitute the values

the measure of angle xoy is equal to

> by central angle

substitute the value