The point P(-4,2) lies on the line segment joining the points A(-4,6) and B (-4,-6).

Explanation

To determine whether the point P(-4, 2) lies on the line segment joining the points A(-4, 6) and B(-4, -6), we can follow these steps:

### Step 1: Identify the coordinates of points A, B, and P.
- Point A has coordinates (-4, 6).
- Point B has coordinates (-4, -6).
- Point P has coordinates (-4, 2).

### Step 2: Check the x-coordinates of points A, B, and P.
- The x-coordinate of point A is -4.
- The x-coordinate of point B is -4.
- The x-coordinate of point P is also -4.

### Step 3: Determine the equation of the line segment AB.
Since both points A and B have the same x-coordinate (-4), the line segment AB is a vertical line described by the equation:
\[ x = -4 \]

### Step 4: Check if point P lies on the line x = -4.
Since point P has the x-coordinate -4, it lies on the line defined by the equation \( x = -4 \).

### Step 5: Check if the y-coordinate of point P is between the y-coordinates of points A and B.
- The y-coordinate of point A is 6.
- The y-coordinate of point B is -6.
- The y-coordinate of point P is 2.

Now, we check if 2 is between -6 and 6:
\[ -6 < 2 < 6 \]
This condition is satisfied.

### Conclusion:
Since point P(-4, 2) has the same x-coordinate as points A and B and its y-coordinate lies between the y-coordinates of points A and B, we conclude that point P lies on the line segment joining A and B. Therefore, the statement is **true**.

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