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find the coordinates of the midpoint of the segment given its endpoint

1) A(5,8) and B(-1,-4)
2) M(-5,9) and N(-2,7)

7 answers

To find the coordinates of the midpoint of a line segment given its endpoints, you can use the midpoint formula:

\[ M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \]

where \((x_1, y_1)\) and \((x_2, y_2)\) are the coordinates of the endpoints.

1) For endpoints A(5, 8) and B(-1, -4):

  • \(x_1 = 5\), \(y_1 = 8\) (for point A)
  • \(x_2 = -1\), \(y_2 = -4\) (for point B)

Using the midpoint formula:

\[ M = \left( \frac{5 + (-1)}{2}, \frac{8 + (-4)}{2} \right) = \left( \frac{4}{2}, \frac{4}{2} \right) = (2, 2) \]

So, the midpoint of segment AB is \(M(2, 2)\).

2) For endpoints M(-5, 9) and N(-2, 7):

  • \(x_1 = -5\), \(y_1 = 9\) (for point M)
  • \(x_2 = -2\), \(y_2 = 7\) (for point N)

Using the midpoint formula:

\[ M = \left( \frac{-5 + (-2)}{2}, \frac{9 + 7}{2} \right) = \left( \frac{-7}{2}, \frac{16}{2} \right) = \left( -\frac{7}{2}, 8 \right) \]

So, the midpoint of segment MN is \(M\left(-\frac{7}{2}, 8\right)\).

Summary of Midpoints:

  1. Midpoint of segment AB is \(M(2, 2)\).
  2. Midpoint of segment MN is \(M\left(-\frac{7}{2}, 8\right)\).
dumb it down

Sure! Let’s break it down step by step in very simple terms.

1) Finding the Midpoint of A(5, 8) and B(-1, -4)

Step 1: Add the x-coordinates together:
\(5 + (-1) = 4\)

Step 2: Divide that sum by 2:
\(\frac{4}{2} = 2\) (this is the x-coordinate of the midpoint)

Step 3: Now do the same for the y-coordinates:
\(8 + (-4) = 4\)

Step 4: Divide that sum by 2:
\(\frac{4}{2} = 2\) (this is the y-coordinate of the midpoint)

Result: The midpoint between A and B is \( (2, 2) \).

2) Finding the Midpoint of M(-5, 9) and N(-2, 7)

Step 1: Add the x-coordinates together:
\(-5 + (-2) = -7\)

Step 2: Divide that sum by 2:
\(\frac{-7}{2} = -\frac{7}{2}\) (this is the x-coordinate of the midpoint)

Step 3: Now do the same for the y-coordinates:
\(9 + 7 = 16\)

Step 4: Divide that sum by 2:
\(\frac{16}{2} = 8\) (this is the y-coordinate of the midpoint)

Result: The midpoint between M and N is \(\left( -\frac{7}{2}, 8 \right)\).

Final Answers:

  1. Midpoint of A and B is \( (2, 2) \).
  2. Midpoint of M and N is \(\left( -\frac{7}{2}, 8 \right)\).
Midpoint of M and N is \(\left( -\frac{7}{2}, 8 \right)\).

Let's clarify the midpoint of points M and N again for accuracy.

We have the points:

  • M(-5, 9)
  • N(-2, 7)

Step 1: Add the x-coordinates:
\[ -5 + (-2) = -7 \]

Step 2: Divide by 2 to get the x-coordinate of the midpoint:
\[ \frac{-7}{2} = -\frac{7}{2} \]

Step 3: Now add the y-coordinates:
\[ 9 + 7 = 16 \]

Step 4: Divide by 2 to get the y-coordinate of the midpoint:
\[ \frac{16}{2} = 8 \]

So, the midpoint of points M and N is indeed:
\[ \left( -\frac{7}{2}, 8 \right) \]

If you have any further questions or if something doesn’t seem right, feel free to ask!

find the coordinates of the midpoint of the segment given its endpoint
1) P (-3,-7) and Q(3,-5)
2) F(2,-6) and G(-8,5)

To find the midpoint of a line segment given its endpoints, we can use the midpoint formula:

\[ M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \]

where \((x_1, y_1)\) and \((x_2, y_2)\) are the coordinates of the endpoints.

1) Finding the Midpoint of P(-3, -7) and Q(3, -5)

  • For point P: \(x_1 = -3\), \(y_1 = -7\)
  • For point Q: \(x_2 = 3\), \(y_2 = -5\)

Using the midpoint formula:

\[ M = \left( \frac{-3 + 3}{2}, \frac{-7 + (-5)}{2} \right) = \left( \frac{0}{2}, \frac{-12}{2} \right) = (0, -6) \]

Result: The midpoint of segment PQ is \(M(0, -6)\).

2) Finding the Midpoint of F(2, -6) and G(-8, 5)

  • For point F: \(x_1 = 2\), \(y_1 = -6\)
  • For point G: \(x_2 = -8\), \(y_2 = 5\)

Using the midpoint formula:

\[ M = \left( \frac{2 + (-8)}{2}, \frac{-6 + 5}{2} \right) = \left( \frac{-6}{2}, \frac{-1}{2} \right) = (-3, -0.5) \]

Result: The midpoint of segment FG is \(M(-3, -0.5)\).

Final Answers:

  1. Midpoint of segment PQ is \(M(0, -6)\).
  2. Midpoint of segment FG is \(M(-3, -0.5)\).