Question

Vertex A from△ABC△ △ A B C is located on the y-axis at the point (0, 4). If A is moved to a new position A' at (3, 5), describe how B and C must be moved to produce a new triangle that has the same orientation and is congruent to the original triangle.

Answer 1

The movement of a point along the coordinate geometry is referred to as translation.

Points B and C must be moved 3 units to the right and 1 unit upward to produce a new triangle that has the same orientation and is congruent to the original triangle.

Given that:

$A = (0,4)$

$A' = (3,5)$

Calculate the movement from A to A',

We simply calculate the difference between the coordinates of A and A'.

For the horizontal movement, we calculate the difference between the x-coordinates

$x = x_2 - x_1$

$x = 3 - 0$

$x = 3$

This implies 3 units to the right

For the vertical movement, we calculate the difference between the y-coordinates

$y = y_2 - y_1$

$y = 5 -4$

$y = 1$

This implies 1 unit upward

Hence, points B and C must be moved 3 units to the right and 1 unit upward to produce a new triangle that has the same orientation and is congruent to the original triangle.

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