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Point P is the midpoint of segment AB. Co-ordinates of P are (1 , 3) and A are (-3 , 8). What are the co-ordinates of point B?
- a)(-5 , -2)
- b)(-5 , 2)
- c)(5 , 2)
- d)(5 , -2)
Correct answer is option 'D'. Can you explain this answer?
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Point P is the midpoint of segment AB. Co-ordinates of P are (1 , 3) a...
Understanding the Midpoint Formula
The midpoint \( P \) of a segment \( AB \) can be calculated using the formula:
\[
P = \left( \frac{x_A + x_B}{2}, \frac{y_A + y_B}{2} \right)
\]
Here, \( P \) is the midpoint, \( A \) has coordinates \( (x_A, y_A) \), and \( B \) has coordinates \( (x_B, y_B) \).
Given Information
- Coordinates of \( P \): (1, 3)
- Coordinates of \( A \): (-3, 8)
Setting Up the Equations
We can use the midpoint formula to create two equations:
1. For the x-coordinates:
\[
1 = \frac{-3 + x_B}{2}
\]
2. For the y-coordinates:
\[
3 = \frac{8 + y_B}{2}
\]
Solving for \( B \)
**For the x-coordinate:**
1. Start with:
\[
1 = \frac{-3 + x_B}{2}
\]
2. Multiply both sides by 2:
\[
2 = -3 + x_B
\]
3. Rearranging gives:
\[
x_B = 2 + 3 = 5
\]
**For the y-coordinate:**
1. Start with:
\[
3 = \frac{8 + y_B}{2}
\]
2. Multiply both sides by 2:
\[
6 = 8 + y_B
\]
3. Rearranging gives:
\[
y_B = 6 - 8 = -2
\]
Coordinates of Point B
Thus, the coordinates of point \( B \) are:
\[
B = (5, -2)
\]
The correct answer is option **D**: \( (5, -2) \).
The midpoint \( P \) of a segment \( AB \) can be calculated using the formula:
\[
P = \left( \frac{x_A + x_B}{2}, \frac{y_A + y_B}{2} \right)
\]
Here, \( P \) is the midpoint, \( A \) has coordinates \( (x_A, y_A) \), and \( B \) has coordinates \( (x_B, y_B) \).
Given Information
- Coordinates of \( P \): (1, 3)
- Coordinates of \( A \): (-3, 8)
Setting Up the Equations
We can use the midpoint formula to create two equations:
1. For the x-coordinates:
\[
1 = \frac{-3 + x_B}{2}
\]
2. For the y-coordinates:
\[
3 = \frac{8 + y_B}{2}
\]
Solving for \( B \)
**For the x-coordinate:**
1. Start with:
\[
1 = \frac{-3 + x_B}{2}
\]
2. Multiply both sides by 2:
\[
2 = -3 + x_B
\]
3. Rearranging gives:
\[
x_B = 2 + 3 = 5
\]
**For the y-coordinate:**
1. Start with:
\[
3 = \frac{8 + y_B}{2}
\]
2. Multiply both sides by 2:
\[
6 = 8 + y_B
\]
3. Rearranging gives:
\[
y_B = 6 - 8 = -2
\]
Coordinates of Point B
Thus, the coordinates of point \( B \) are:
\[
B = (5, -2)
\]
The correct answer is option **D**: \( (5, -2) \).
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Point P is the midpoint of segment AB. Co-ordinates of P are (1 , 3) a...
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Point P is the midpoint of segment AB. Co-ordinates of P are (1 , 3) and A are (-3 , 8). What are the co-ordinates of point B?a)(-5 , -2)b)(-5 , 2)c)(5 , 2)d)(5 , -2)Correct answer is option 'D'. Can you explain this answer?
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