First slide

Cartesian plane

Question

Two vertices of a triangle are (4, -3) and (-2, 5). If the orthocenter of the triangle is at (1,2),then the third vertex is

Moderate

A

(-33, -26)
B

(33, 26)
C

(26,33)
D

none of these

Solution

Let the third vertex be (h, k).
Now, the slope of AD is (k - 2)/(h - 1), the slope of BC is (5 + 3)l(-2 - 4)=4/3, the slope of BE is (-3 -2)/(4 - 1) = 5/3, and the
slope of AC is (k - 5)/(h + 2).
Since $AD ⊥ BC,$
we have $\frac{k - 2}{h - 1} \times \frac{- 4}{3} = - 1$
or 3h-4k+5=0 (i)
Again, since $BE ⊥ AC$ , we have
$- \frac{5}{3} \times \frac{k - 5}{h + 2} = - 1$
or 3h - 5k +31 = 0 (ii)
On solving (i) and (ii), we get h=33, k=26.Hence, the third vertex is (33, 26).

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