SATHEE: Properties of Triangles 3 Question 1

Properties of Triangles 3 Question 1

1. Two vertices of a triangle are $(0, 2)$ and $(4, 3)$ . If its orthocentre is at the origin, then its third vertex lies in which quadrant?

(2019 Main, 10 Jan II)

(a) Fourth

(b) Third

(d) First

Show Answer

Answer:

Correct Answer: 1. (c)

Solution:

Let $A B C$ be a given triangle with vertices $B (0, 2), C (4, 3)$ and let third vertex be $A (a, b)$

$(0, 2)$

Also, let $D, E$ and $F$ are the foot of perpendiculars drawn from $A, B$ and $C$ respectively.

Then, $A D ⊥ B C \Rightarrow \frac{b - 0}{a - 0} \times \frac{3 - 2}{4 - 0} = - 1$

[if two lines having slopes $m_{1}$ and $m_{2}$ , are

$\begin{array}{lc} \Rightarrow & b + 4 a = 0 \\ and & C F ⊥ A B \\ \Rightarrow & \frac{b - 2}{a - 0} \times \frac{3 - 0}{4 - 0} = - 1 \\ \Rightarrow & 3 b - 6 = - 4 a \\ \Rightarrow & 4 a + 3 b = 6 \end{array}$

From Eqs. (i) and (ii), we get

$- b + 3 b = 6 \Rightarrow 2 b = 6$

$\begin{array}{lll} \Rightarrow & b & = 3 \\ and & a = - \frac{3}{4} \end{array}$

So, the third vertex

$(a, b) \equiv - \frac{3}{4}, 3$ , which lies in II quadrant.

Properties of Triangles 3 Question 1

1. Two vertices of a triangle are $(0, 2)$ and $(4, 3)$ . If its orthocentre is at the origin, then its third vertex lies in which quadrant?

Answer:

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Properties of Triangles 3 Question 1

1. Two vertices of a triangle are (0,2) and (4,3). If its orthocentre is at the origin, then its third vertex lies in which quadrant?

Answer:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

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1. Two vertices of a triangle are $(0, 2)$ and $(4, 3)$ . If its orthocentre is at the origin, then its third vertex lies in which quadrant?