I see you've uploaded two images. Let me analyze the math-related content in them and provide detailed explanations.

Image 1:

The question asks if the lines $AB$ and $AC$ are perpendicular, where the points are given as:

• $A(3, 6)$,
• $B(6, 3)$,
• $C(2, 1)$.

To determine if the lines are perpendicular, we calculate the slopes of the lines $AB$ and $AC$ and check if their product equals $-1$.

1. Slope of $AB$: The slope of a line between two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by: $m = \frac{y_2 - y_1}{x_2 - x_1}.$ For $A(3, 6)$ and $B(6, 3)$: $m_{AB} = \frac{3 - 6}{6 - 3} = \frac{-3}{3} = -1.$

2. Slope of $AC$: Using $A(3, 6)$ and $C(2, 1)$: $m_{AC} = \frac{1 - 6}{2 - 3} = \frac{-5}{-1} = 5.$

3. Checking perpendicularity: Two lines are perpendicular if the product of their slopes is $-1$. For $AB$ and $AC$: $m_{AB} \cdot m_{AC} = (-1) \cdot 5 = -5.$ Since the product is not $-1$, the lines are not perpendicular.

Answer for Image 1: Неверно (False)

Image 2:

The question asks for the value of $q$ such that the line $2x - 4y + q = 0$ passes through the point $(2, 3)$.

1. Substitute $x = 2$ and $y = 3$ into the equation: $2(2) - 4(3) + q = 0.$

2. Simplify the equation: $4 - 12 + q = 0.$

3. Solve for $q$: $q = 12 - 4 = 8.$

Answer for Image 2: $q = 8$

Let me know if you'd like more details or further explanation on these solutions. Here are some related questions to explore:

1. How do we determine if three points lie on the same line?
2. What is the general formula for the equation of a line passing through two points?
3. Can two perpendicular lines have the same y-intercept? Why or why not?
4. How do we find the distance between a point and a line in the coordinate plane?
5. What is the geometric interpretation of the slope in terms of angle with the x-axis?

Tip: Always verify perpendicularity by calculating slopes carefully and ensuring their product is exactly $-1$.