Question

1. reflect the figure through l (1, 2)

Explanation:

Step1: Identify original coordinates

From the grid:

• $L=(1, 2)$
• $Q=(4, -1)$
• $G=(3, 5)$

Step2: Reflection formula over point

For a point $(x,y)$ reflected over $(a,b)$, the image $(x',y')$ is:
$$x' = 2a - x, \quad y' = 2b - y$$

Step3: Calculate $L'$

Reflect $L$ over itself:
$x' = 2(1) - 1 = 1$, $y' = 2(2) - 2 = 2$
$L'=(1,2)$

Step4: Calculate $Q'$

Reflect $Q$ over $L(1,2)$:
$x' = 2(1) - 4 = -2$, $y' = 2(2) - (-1) = 5$
$Q'=(-2,5)$

Step5: Calculate $G'$

Reflect $G$ over $L(1,2)$:
$x' = 2(1) - 3 = -1$, $y' = 2(2) - 5 = -1$
$G'=(-1,-1)$

Answer:

$L'(1, 2)$
$Q'(-2, 5)$
$G'(-1, -1)$