Math Problem Statement

find the midpoint of the line: a= (-3,-3) b= (3,1)

Solution

To find the midpoint of the line segment connecting the points A(3,3)A(-3, -3) and B(3,1)B(3, 1), you can use the midpoint formula. The midpoint (M)(M) of a line segment with endpoints (x1,y1)(x_1, y_1) and (x2,y2)(x_2, y_2) is given by:

M=(x1+x22,y1+y22)M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)

For the given points A(3,3)A(-3, -3) and B(3,1)B(3, 1), we have:

x1=3,y1=3,x2=3,y2=1x_1 = -3, \quad y_1 = -3, \quad x_2 = 3, \quad y_2 = 1

Plugging these values into the midpoint formula:

M=(3+32,3+12)M = \left( \frac{-3 + 3}{2}, \frac{-3 + 1}{2} \right)

Calculate each coordinate:

M=(02,22)M = \left( \frac{0}{2}, \frac{-2}{2} \right) M=(0,1)M = (0, -1)

Therefore, the midpoint of the line segment connecting A(3,3)A(-3, -3) and B(3,1)B(3, 1) is (0,1)(0, -1).

Would you like more details or have any questions?

Here are 8 related questions to explore further:

  1. How do you find the distance between two points in the coordinate plane?
  2. What is the formula for finding the slope of a line segment between two points?
  3. How can you determine if a point is the midpoint of a line segment?
  4. What is the midpoint of the line segment with endpoints (5,2)(5, 2) and (1,6)(-1, 6)?
  5. How do you find the equation of a line given two points?
  6. What is the significance of the midpoint in geometry?
  7. How can you use the midpoint formula in real-world applications?
  8. What are some examples of problems where finding the midpoint is useful?

Tip: When using the midpoint formula, ensure you correctly add and divide the coordinates of the endpoints to avoid errors.