Question

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Given:

∆ABC is a right-angle triangle with vertices A(6;7), B(m;n) and C(1;2).


AB is a vertical line and BC is a horizontal line.

1) determine the coordinate of B

2) determine the coordinate of C


3) Describe the transformation from ABC to A’ B’ C’

4) write an algebraic rule for the transformation from ABC to A’ B’ C’

5) If P is reflected about the line y= x, determine the new coordinate


6! write an algebraic rule for reflection about the line y = x for any coordinate

Answer 1

0

Explanation:

010001001101010011000001111

Answer 2

1. The coordinates of B is (6, 2)

2. The coordinate of C' is (-5, -5)

3. The transformation from ABC to A’ B’ C’ is

• Translation 6 units to the left and 7 units down

4. The algebraic rule is (x - 6, y - 7)

5. The new coordinate of P (-2, 4)

6. Algebraic rule for reflection about the line y = x is (x, y) → (y, x)

How to find the coordinates

The coordinates of B is sought as follows

• A and B share same x-axis, so m = 6

• C and B share same y-axis, so n = 2

The new coordinates of C (1, 2) → (1 - 6, 2 - 7) → (-5, -5)

Investigating the image we find the algebraic rule to be Translation 6 units to the left and 7 units down which is represented as (x - 6, y - 7)

Applying the rule (x, y) → (y, x) coordinates of P' is found to be (-2, 4)