Find the coordinate of the point at which the perpendicular bisector of the line joining (2,7) to (10,3) meet the x- axis please solve through making the diagram of line point etc?

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Find the coordinate of the point at which the perpendicular bisector of the line joining (2,7) to (10,3) meet the x- axis please solve through making the diagram of line point etc?

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Answer 1 · 2018-04-30T14:22:42

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The coordinates of the mid point of the line joining (2,7) to (10,3) are $(\frac{2 + 10}{2}, \frac{7 + 3}{2}) \equiv (6, 5)$ $((2+10)/2,(7+3)/2)equiv(6,5)$

Let the coordinates of the point of intersection of the perpendicular bisector of the line segment joining the two given point be $(h, 0)$ $(h,0)$ .

So the gradient of the perpendicular bisector $\frac{5 - 0}{6 - h} = \frac{5}{6 - h}$ $(5-0)/(6-h)=5/(6-h)$

Again the slope of the line segment is $= \frac{7 - 3}{2 - 10} = - \frac{1}{2}$ $=(7-3)/(2-10)=-1/2$

As the bisector is perpendicular to the line segment then

$\frac{5}{6 - h} \times (- \frac{1}{2}) = - 1$ $5/(6-h)xx(-1/2)=-1$

$\Rightarrow 5 = 12 - 2 h$ $=>5=12-2h$

$\Rightarrow h = \frac{7}{2} = 3.5$ $=>h=7/2=3.5$

So the coordinates of the point of intersection of the perpendicular bisector with the X-axis is $(3.5, 0)$ $(3.5,0)$

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Find the coordinate of the point at which the perpendicular bisector of the line joining (2,7) to (10,3) meet the x- axis please solve through making the diagram of line point etc?

1 Answer

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