https://file.aiquickdraw.com/mathbot/file/1726495114341ho4vpnis.jpg

The problem in the image translates to:

"If the points \( P(7, 3) \), \( Q(-3, 1) \), and \( R(2, -3) \) lie in a Cartesian plane, what is the position of point \( Q \) relative to the line PR?"

### Solution:
We can determine the position of point \( Q \) relative to line \( PR \) by checking if it lies on the line, is above the line, or is below the line.

1. **Equation of Line PR:**
   To find the equation of line PR, we first calculate the slope \( m \) using points \( P(7, 3) \) and \( R(2, -3) \):
   \[
   m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-3 - 3}{2 - 7} = \frac{-6}{-5} = \frac{6}{5}
   \]
   
   Using the point-slope form of the equation of a line, \( y - y_1 = m(x - x_1) \), and substituting \( P(7, 3) \) and \( m = \frac{6}{5} \):
   \[
   y - 3 = \frac{6}{5}(x - 7)
   \]
   Expanding:
   \[
   y - 3 = \frac{6}{5}x - \frac{42}{5}
   \]
   \[
   y = \frac{6}{5}x - \frac{42}{5} + 3 = \frac{6}{5}x - \frac{42}{5} + \frac{15}{5} = \frac{6}{5}x - \frac{27}{5}
   \]
   So, the equation of line PR is:
   \[
   y = \frac{6}{5}x - \frac{27}{5}
   \]

2. **Position of Point Q:**
   Now, substitute the coordinates of point \( Q(-3, 1) \) into the equation of line PR:
   \[
   y = \frac{6}{5}(-3) - \frac{27}{5} = \frac{-18}{5} - \frac{27}{5} = \frac{-45}{5} = -9
   \]
   
   Since the y-coordinate of point \( Q \) is 1, and the value of \( y \) on the line PR when \( x = -3 \) is \( -9 \), point \( Q \) does not lie on the line and is above the line because \( 1 > -9 \).

### Answer:
Point \( Q \) is **above** the line PR.

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Would you like further details or have any questions? Here are five related questions to deepen your understanding:

1. How would you determine the equation of a line passing through two different points?
2. What does the slope of a line represent geometrically?
3. How can we verify whether a point lies on a specific line?
4. How do you calculate the perpendicular distance from a point to a line?
5. What other methods can you use to find the relative position of a point to a line?

### Tip:
For any line in the Cartesian plane, the relative position of a point can be determined by comparing the y-coordinate of the point with the value given by the line equation at the same x-coordinate.

Jika titik P(7,3), Q(-3,1), dan R(2,-3) berada pada satu bidang Cartesius, maka kedudukan titik Q terhadap garis PR adalah ....

Find out how to determine the relative position of point Q(-3, 1) with respect to the line passing through points P(7, 3) and R(2, -3) in a Cartesian plane. Learn how to calculate the slope of a line and use the point-slope formula to solve the problem. Suitable for Grades 9-10.

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