Question

Triangle ABC with vertices A (-1, 4), B( -4, 1), and C(-1, 1) is reflected across the y-axis and then translated 4 units to the left to form triangle A’B’C’. What are the coordinates of the vertices of triangle A’B’C’?
A
A’ (1, 4), B’ (4, 1), C’ (1, 1)
B
A’ (-3, 4), B’ (0, 1), C’ (-3, 1)
C
A’ (-1, -4), B’ (-4, -1), C’ (-1, -1)
D
A’ (-5, -4), B’ (-8, -1), C’ (-5, -1)

Answer 1

Given:

Triangle ABC with vertices A (-1, 4), B( -4, 1), and C(-1, 1) is reflected across the y-axis and then translated 4 units to the left to form triangle A’B’C’.

To find:

The coordinates of the vertices of triangle A’B’C’.

Solution:

If triangle ABC reflected across y-axis, then

$(x,y)\to (-x,y)$

$A(-1,4)\to A_1(1,4)$

$B(-4,1)\to B_1(4,1)$

$C(-1,1)\to C_1(1,1)$

Coordinates of image after reflection across y-axis are $A_1(1,4),B_1(4,1),C_1(1,1).$

Then triangle translated 4 units to the left to form triangle A’B’C’.

$(x,y)\to (x-4,y)$

$A_1(1,4)\to A'(-3,4)$

$B_1(4,1)\to B'(0,1)$

$C_1(1,1)\to C'(-3,1)$

Therefore, the vertices of triangle A’B’C’ are A’ (-3, 4), B’ (0, 1), C’ (-3, 1).

Hence, the correct option is B.