KnowledgeBoat Logo
|

Mathematics

In the given graph, P and Q are points such that PQ cuts off intercepts of 5 units and 3 units along the x-axis and y-axis respectively. Line RS is perpendicular to PQ and passes through the origin. Find the:

(a) coordinates of P and Q

(b) equation of line RS

In the given graph, P and Q are points such that PQ cuts off intercepts of 5 units and 3 units along the x-axis and y-axis respectively. Line RS is perpendicular to PQ and passes through the origin. Find the: ICSE 2025 Maths Solved Question Paper.

Straight Line Eq

7 Likes

Answer

(a) Given,

PQ cuts off intercepts of 5 units and 3 units along the x-axis and y-axis respectively.

Thus,

Coordinates of P = (5, 0) and coordinates of Q = (0, -3).

Hence, coordinates of P = (5, 0) and coordinates of Q = (0, -3).

(b) By formula,

Slope (m) = −y2−y1x2−x1-\dfrac{y2 - y1}{x2 - x1}

⇒ Slope of PQ = mPQ = −3−00−5=−3−5=35\dfrac{-3 - 0}{0 - 5} = \dfrac{-3}{-5} = \dfrac{3}{5}.

We know that,

Product of slopes of perpendicular lines = -1.

⇒ Slope of RS × Slope of PQ = -1

⇒ Slope of RS × 35\dfrac{3}{5} = -1

⇒ Slope of RS = −53-\dfrac{5}{3}.

By point-slope formula,

Equation of line : y−y1=m(x−x1)y - y{1} = m(x - x{1})

Since, slope of RS = −53-\dfrac{5}{3} and it passes through the origin.

Equation of RS :

⇒ y−0=−53(x−0)y - 0 = -\dfrac{5}{3}(x - 0)

⇒ y = −53x-\dfrac{5}{3}x

⇒ 3y = -5x

⇒ 5x + 3y = 0.

Hence, the equation of line RS is 5x + 3y = 0.

Answered By

3 Likes

Related Questions