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