Find the coordinates of the mid-point of x and y intercepts of the line 2y = 4x - 8

  • A (2, 0)
  • B (1, -2)
  • C (-1, -2)
  • D (1, 2)

The correct answer is B. (1, -2)

To find the x-intercept, we set \(y = 0\) in the equation \(2y = 4x - 8\):

2 \cdot 0 = 4x - 8.\)

Solving for \(x\):

0 = 4x - 8 \Rightarrow 4x = 8 \Rightarrow x = 2.\)

So, the x-intercept is \((2, 0)\).

To find the y-intercept, we set \(x = 0\) in the equation \(2y = 4x - 8\):

2y = 4 \cdot 0 - 8.\)

Solving for \(y\):

2y = -8 \Rightarrow y = -4.\)

So, the y-intercept is \((0, -4)\).

The midpoint of two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by the formula:

Midpoint \(\left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right)\).

For the x-intercept \((2, 0)\) and the y-intercept \((0, -4)\), the midpoint is:

Midpoint \(\left(\frac{2 + 0}{2}, \frac{0 + (-4)}{2}\right) = (1, -2)\).

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