Question

the vertices of \\( \triangle abc \\) are \\( a(-3, 4) \\), \\( b(-2, 5) \\), and \\( c(-4, 2) \\). if \\( \triangle abc \\) is reflected across the line \\( y = -2 \\) to produce the image \\( \triangle abc \\), find the coordinates of the vertex \\( b \\). (type an ordered pair.) the coordinates of \\( b \\) after a reflection across the line \\( y = -2 \\) are \\( \square \\).

Explanation:

Step1: Identify original point B

Original coordinates: $B(-2, 5)$

Step2: Calculate distance to $y=-2$

Distance = $5 - (-2) = 7$

Step3: Find new y-coordinate

New $y = -2 - 7 = -9$

Step4: Keep x-coordinate unchanged

$x = -2$

Answer:

$(-2, -9)$