Find the distance of the point $(1, 2)$ from the midpoint of the line segment joining the points $(6, 8)$ and $(2, 4)$

5

units

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4

units

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3

units

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2

units

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Solution

The correct option is A $5$ units
Mid point of two points ${(x}_{1}, y_{1})$ and ${(x}_{2}, y_{2})$ is calculated by the formula $(\frac{x_{1} + x_{2}}{2}, \frac{y_{1} + y_{2}}{2})$

Using this formula, mid point of $(6, 8)$ and $(2, 4) = (\frac{6 + 2}{2}, \frac{8 + 4}{2}) = (4, 6)$

Distance between two points $(x_{1}, y_{1})$ and $(x_{2}, y_{2})$ can be calculated using the formula $\sqrt{{(x_{2} - x_{1})}_{2}^{2} + {(y_{2} - y_{1})}_{2}^{2}}$

Distance between the points $(1, 2)$ and D $(4, 6) = \sqrt{{(1 - 4)}^{2} + {(2 - 6)}^{2}} = \sqrt{9 + 16} = \sqrt{25} = 5$

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Find the distance of the point (1,2) from the midpoint of the line segment joining the points (6,8) and (2,4)

Find the distance of the point $(1, 2)$ from the midpoint of the line segment joining the points $(6, 8)$ and $(2, 4)$