SATHEE: Straight Line and Pair of Straight Lines 3 Question 2

Straight Line and Pair of Straight Lines 3 Question 2

3. Two sides of a rhombus are along the lines, $x - y + 1 = 0$ and $7 x - y - 5 = 0$ . If its diagonals intersect at $(- 1, - 2)$ , then which one of the following is a vertex of this rhombus?

(2016 Main)

(a) $(- 3, - 9)$

(b) $(- 3, - 8)$

(d) $- \frac{10}{3}, - \frac{7}{3}$

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Answer:

Correct Answer: 3. (c)

Solution:

As the given lines $x - y + 1 = 0$ and $7 x - y - 5 = 0$ are not parallel, therefore they represent the adjacent sides of the rhombus.

On solving $x - y + 1 = 0$ and $7 x - y - 5 = 0$ , we get $x = 1$ and $y = 2$ . Thus, one of the vertex is $A (1, 2)$ .

$(1, 2)$

Let the coordinate of point $C$ be $(x, y)$ .

$\begin{aligned} Then, & - 1 & = \frac{x + 1}{2} and - 2 = \frac{y + 2}{2} \\ \Rightarrow & x + 1 & = - 2 and y = - 4 - 2 \\ \Rightarrow & x & = - 3 \\ and & y & = - 6 \end{aligned}$

Hence, coordinates of $C = (- 3, - 6)$

Note that, vertices $B$ and $D$ will satisfy $x - y + 1 = 0$ and $7 x - y - 5 = 0$ , respectively.

Since, option (c) satisfies $7 x - y - 5 = 0$ , therefore coordinate of vertex $D$ is $\frac{1}{3}, \frac{- 8}{3}$ .

Straight Line and Pair of Straight Lines 3 Question 2

3. Two sides of a rhombus are along the lines, $x - y + 1 = 0$ and $7 x - y - 5 = 0$ . If its diagonals intersect at $(- 1, - 2)$ , then which one of the following is a vertex of this rhombus?

Answer:

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Straight Line and Pair of Straight Lines 3 Question 2

3. Two sides of a rhombus are along the lines, x−y+1=0 and 7x−y−5=0. If its diagonals intersect at (−1,−2), then which one of the following is a vertex of this rhombus?

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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3. Two sides of a rhombus are along the lines, $x - y + 1 = 0$ and $7 x - y - 5 = 0$ . If its diagonals intersect at $(- 1, - 2)$ , then which one of the following is a vertex of this rhombus?