Question 20 of 25intermediate🔧 ApplyNumerical3 marks

Use the connection you found to find the coordinates of B given that M (−7, 1) is the midpoint of A (3, −4) and B (x, y).

Correct Answer

(-17, 6)

Exercise: END-OF-CHAPTER EXERCISES | Q: *10 | (Page 13)
For More Understanding

Explanation

The question requires applying the midpoint formula, which is the 'connection' between the coordinates of the midpoint and the endpoints of a segment. The midpoint M(x, y) of a segment joining A(x₁, y₁) and B(x₂, y₂) is given by x = (x₁ + x₂)/2 and y = (y₁ + y₂)/2. By substituting the given values of M and A, we can solve for the unknown coordinates of B.

Solution Steps

  1. Step 1: Midpoint Connection: The coordinates of the midpoint M of a segment joining A(x₁, y₁) and B(x₂, y₂) are given by M = ((x₁ + x₂)/2, (y₁ + y₂)/2).

  2. Step 2: x-coordinate equation: For the x-coordinate, we have -7 = (3 + x)/2.

  3. Step 3: Solve for x: Multiplying by 2 gives -14 = 3 + x. Subtracting 3 from both sides, x = -17.

  4. Step 4: y-coordinate equation: For the y-coordinate, we have 1 = (-4 + y)/2.

  5. Step 5: Solve for y: Multiplying by 2 gives 2 = -4 + y. Adding 4 to both sides, y = 6.

  6. Step 6: Coordinates of B: Therefore, the coordinates of point B are (-17, 6).

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