Cartesian plane

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Question

The distance between the circumcenter and the orthocenter of the triangle whose vertices are (0, 0), (6, 8), and (4,3) is Z. Then the value of $\frac{L}{\sqrt{5}}$ is _________ .

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Solution

Given vertices of triangle are o(0,0), B(6,8), and c(-4,3).
Slope of OB = $\frac{8}{6}$
Slope of OC = $- \frac{3}{4}$
$∴ ∠ BOC = \frac{π}{2}$
$ΔOBC$ is right-angled at O.
Circumcenter = Midpoint of hypotenuse BC = $(1, \frac{11}{2})$
Orthocenter - Vertex O(0, 0)
Required distance = $\sqrt{(1 + \frac{121}{4})} = \frac{5 \sqrt{5}}{2} units$

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Cartesian plane

Remember concepts with our Masterclasses.

The distance between the circumcenter and the orthocenter of the triangle whose vertices are (0, 0), (6, 8), and (4,3) is Z. Then the value of L5 is _________ .

Given vertices of triangle are o(0,0), B(6,8), and c(-4,3).Slope of OB = 86Slope of OC = −34∴∠BOC=π2ΔOBC is right-angled at O.Circumcenter = Midpoint of hypotenuse BC = 1,112Orthocenter - Vertex O(0, 0)Required distance = 1+1214=552 units

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The distance between the circumcenter and the orthocenter of the triangle whose vertices are (0, 0), (6, 8), and (4,3) is Z. Then the value of $\frac{L}{\sqrt{5}}$ is _________ .