If the midpoint of a line segment joining (3, | vedclass

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Question

(D) The midpoint formula for a line segment joining $(x_1, y_1)$ and $(x_2, y_2)$ is given by $\left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right)$.

Vedclass · Accepted Answer

$5$

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(D) The midpoint formula for a line segment joining $(x_1, y_1)$ and $(x_2, y_2)$ is given by $\left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right)$.Given the points $(3, 4)$ and $(a, 8)$,the midpoint is $\left(\frac{3 + a}{2}, \frac{4 + 8}{2}\right)$.We are given that the midpoint is $(4, 6)$.Equating the coordinates,we get $\left(\frac{3 + a}{2}, \frac{12}{2}\right) = (4, 6)$.This simplifies to $\left(\frac{3 + a}{2}, 6\right) = (4, 6)$.Comparing the $x$-coordinates: $\frac{3 + a}{2} = 4$.Multiplying by $2$,we get $3 + a = 8$.Therefore,$a = 8 - 3 = 5$.

If the midpoint of a line segment joining $(3, 4)$ and $(a, 8)$ is $(4, 6)$,then $a = \ldots$

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