Type the correct answer in each box. spell all the words correctly, and use numerals instead of words for numbers. if necessary, use / for the fraction bar(s).we can show that ∆abc is congruent to ∆a′b′c′ by a translation of unit(s) and a across the -axis.

Solution-

Rules of translation and reflection-

When translating a point h units to left, we apply the rule (x, y) → (x-h, y),

When translating a point h units to right, we apply the rule (x, y) → (x+h, y),

When reflecting a point around x-axis, we apply the rule (x, y) → (x, -y),

When reflecting a point around y-axis, we apply the rule (x, y) → (-x, y).

The co-ordinates of the vertices of the ΔABC,

A = (8, 8)

B = (10, 4)

C = (2, 6)

The co-ordinates of the vertices of the ΔA'B'C',

A' = (6, -8)

B' = (8, -4)

C' = (0, -6)

As we can notice that all the x co-ordinates of the vertices are reduced by 2 units and the sign of y co-ordinates are changed. So the triangle was translated 2 units to left, first and then reflected around x axis.

Translated 2 units to the left and Reflected across x-axis

Step-by-step explanation:

We are given that,

Triangle ABC is transformed to triangle A'B'C'.

From the graph, we see that,

The co-ordinates of ΔABC are A(8,8), B(10,4) and C(2,6).

The co-ordinates of ΔA'B'C' are A(6,-8), B(8,-4) and C(0,-6).

So, we get that,

A = (8,8) → A' = (6,-8)

B = (10,4) → A' = (8,-4)

C= (2,6) → A' = (0,-6)

That is,

'The x co-ordinate is subtracted by 2 and the y co-ordinate is multiplied by negative sign'.

That is, the rule of transformation is (x,y) becomes (x-2,-y).

Which means, the triangle ABC is translated 2 units to the left and is reflected across x-axis to obtain A'B'C'.