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The midpoint of the segment of the line y = 4x + 3 which lies between the x-ax 1...


Question

The midpoint of the segment of the line y = 4x + 3 which lies between the x-ax 1 is and the y-ax 1 is

Options

A) (\(\frac{3}{2}\), \(\frac{3}{2}\))

B) (\(\frac{2}{3}\), \(\frac{3}{2}\))

C) (\(\frac{3}{8}\), \(\frac{3}{2}\))

D) (-\(\frac{3}{8}\), \(\frac{3}{2}\))

The correct answer is D.

Explanation:

y = 4x + 3
when x = 0, y = 3 \(\to\) (0, 3)
when y = 0, x = -\(\frac{3}{4}\) \(\to\) (\(\frac{3}{4}\), 0)
mid-point \(\frac{0 + (-{\frac{3}{4}})}{2}\), \(\frac{3 + 0}{4}\)
-\(\frac{3}{8}\), \(\frac{3}{2}\)

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Dicussion (1)

  • y = 4x + 3
    when x = 0, y = 3 \(\to\) (0, 3)
    when y = 0, x = -\(\frac{3}{4}\) \(\to\) (\(\frac{3}{4}\), 0)
    mid-point \(\frac{0 + (-{\frac{3}{4}})}{2}\), \(\frac{3 + 0}{4}\)
    -\(\frac{3}{8}\), \(\frac{3}{2}\)

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