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The problem is asking to determine whether the lines passing through pairs of points are perpendicular ("serenjang" in Malay).

To check if two lines are perpendicular, their slopes (\(m\)) must satisfy the condition:
\[
m_1 \times m_2 = -1
\]
where \(m_1\) and \(m_2\) are the slopes of the two lines.

### Points:
- \(A(-2, 5)\), \(B(4, 2)\)
- \(C(-1, -2)\), \(D(3, 6)\)

### Step 1: Calculate slope of line AB.
The slope of a line passing through 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 points \(A(-2, 5)\) and \(B(4, 2)\):
\[
m_{AB} = \frac{2 - 5}{4 - (-2)} = \frac{-3}{6} = -\frac{1}{2}
\]

### Step 2: Calculate slope of line CD.
For points \(C(-1, -2)\) and \(D(3, 6)\):
\[
m_{CD} = \frac{6 - (-2)}{3 - (-1)} = \frac{8}{4} = 2
\]

### Step 3: Check if the lines are perpendicular.
Now, check the product of the slopes:
\[
m_{AB} \times m_{CD} = \left(-\frac{1}{2}\right) \times 2 = -1
\]
Since the product is \(-1\), the lines passing through points \(A\), \(B\) and \(C\), \(D\) are indeed perpendicular.

Would you like further details or have any questions?

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Here are 5 related questions:
1. How do you find the slope of a line given two points?
2. What is the geometric meaning of two lines being perpendicular?
3. Can the slopes of two parallel lines ever be negative reciprocals?
4. How would the method change if the points given were collinear?
5. How can we apply the concept of slopes to determine if two vectors are orthogonal?

**Tip:** When checking if two lines are perpendicular, always calculate their slopes first. If their product is \(-1\), the lines are perpendicular.

Tentukan samada garis-garis yang melalui pasangan titik-titik adalah serenjang. A(-2, 5), B(4, 2) dan C(-1, -2), D(3, 6).

This problem involves determining whether two lines passing through points A(-2, 5), B(4, 2) and C(-1, -2), D(3, 6) are perpendicular. Using slope calculations and checking the perpendicularity condition (m1 * m2 = -1), students will explore key concepts in analytic geometry.

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