First slide

Cartesian plane

Question

Orthocentre of the triangle with vertices $(0, 0), (3, 4)$ and $(4, 0)$ is

Moderate

A

$(3, 5 / 2)$
B

$(3, 12)$
C

$(3, 3 / 4)$
D

$(3, 9)$

Solution

The coordinates of the centroid G and circumcentre O of the triangle are $(7 / 3, 4 / 3)$ and $(2, 13 / 8)$ respectively. We know that the circumcentre G divides the segment joining the orthocentre O' and circumcentre O in the ratio 2 : 1. Therefore, if (x, y) are the coordinates of the orthocentre then
$\frac{x + 4}{3} = \frac{7}{3}$ and $\frac{y + \frac{13}{4}}{3} = \frac{4}{3} \Rightarrow x = 3$ and $y = \frac{3}{4}$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App