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To solve this problem, we need to determine the position of point \( P(29, 26) \) relative to the line segment \( JK \), where \( J(11, 53) \) and \( K(41, 8) \).

### Step 1: Equation of Line Segment \( JK \)
The first step is to find the equation of the line passing through points \( J \) and \( K \). The slope of the line \( JK \) is given by:

\[
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{8 - 53}{41 - 11} = \frac{-45}{30} = -1.5
\]

Now, using the point-slope form of the line equation, we can substitute one of the points (say \( J(11, 53) \)) and the slope \( m = -1.5 \):

\[
y - y_1 = m(x - x_1)
\]

Substituting \( x_1 = 11 \), \( y_1 = 53 \), and \( m = -1.5 \):

\[
y - 53 = -1.5(x - 11)
\]

Simplifying:

\[
y = -1.5x + 16.5 + 53
\]
\[
y = -1.5x + 69.5
\]

So the equation of the line \( JK \) is:

\[
y = -1.5x + 69.5
\]

### Step 2: Check if Point \( P(29, 26) \) Lies on Line \( JK \)
Now, we substitute the \( x \)-coordinate of point \( P(29, 26) \) into the equation of the line to check if it lies on the line:

\[
y = -1.5(29) + 69.5 = -43.5 + 69.5 = 26
\]

Since the \( y \)-coordinate of point \( P \) is also 26, this shows that point \( P(29, 26) \) lies on the line segment \( JK \).

### Step 3: Determine the Position of \( P \) on the Line Segment
To confirm whether point \( P(29, 26) \) is between points \( J(11, 53) \) and \( K(41, 8) \), we can check the \( x \)-coordinates. Point \( P \) has an \( x \)-coordinate of 29, which lies between 11 (the \( x \)-coordinate of \( J \)) and 41 (the \( x \)-coordinate of \( K \)).

Therefore, point \( P(29, 26) \) is on the line segment \( JK \) and lies between points \( J \) and \( K \).

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Would you like further explanation on any step, or any more details on how the calculations were made?

### Related Questions:
1. How do you find the distance between two points in a plane?
2. How can you use vectors to describe the position of a point on a line?
3. What is the midpoint formula, and how does it relate to this problem?
4. How would the equation change if the line was vertical or horizontal?
5. How can you calculate the perpendicular distance from a point to a line?

#### Tip:
Always visualize points and lines on the Cartesian plane to better understand their relative positions.

Point P(29, 26) is a point on line segment JK in the Cartesian plane, where J(11, 53) and K(41, 8). Which of the following statements describes the position of point P?

Learn how to determine the position of point P(29, 26) on the line segment between points J(11, 53) and K(41, 8) in the Cartesian plane. This problem involves calculating the slope of the line and verifying if the point lies on the segment. Suitable for students in Grades 8-10.

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