Question

Find the slope of a line, which passes through the origin, and the mid-point of the line segment joining the points P (0, -4) and B (8, 0).

Answer 1

Given:

The required line passes through:
• The origin O(0, 0)
• The midpoint of the line segment joining P(0, −4) and B(8, 0)

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Step 1: Find the midpoint of PB

Midpoint formula:

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

For P(0, −4) and B(8, 0):

Midpoint = \(\left(\frac{0+8}{2}, \frac{-4+0}{2}\right)\)

Midpoint = (4, −2)

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Step 2: Find the slope of the line

Slope of the line passing through points (0,0) and (4, −2):

m = (y₂ − y₁) / (x₂ − x₁)

m = (−2 − 0) / (4 − 0)

m = −2 / 4

m = −1/2

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Final Answer:

The slope of the required line is −1/2.