First slide

Equation of line in Straight lines

Question

A rectangle has two opposite vertices at the points (1, 2) and (5, 5). If the other vertices lie on the line x = 3, then the coordinates of the other vertices are

Moderate

A

(3, –1), (3, –6)
B

(3, 1), (3, 5)
C

(3, 2), (3, 6)
D

(3, 1), (3, 6)

Solution

Let A ≡ (1, 2) and C ≡ (5, 5). Since the vertices B and D lie on the line x = 3, therefore, let B ≡ (3, y₁) and D ≡ (3, y₂).
Since AC and BD bisect each other, so they have same middle point
$i . e, \frac{y_{1} + y_{2}}{2} = \frac{2 + 5}{2}$
$o r y_{1} + y_{2} = 7$ (1)
Also, BD² = AC²
⇒ (y₁ – y₂)² = (1 – 5)² + (2 – 5)² = 25
or y₁ – y₂ = ± 5 (2)
Solving (1) and (2), we get y₁= 6, y₂ = 1 or y₁ = 1, y₂ = 6
Thus, the other vertices of the rectangle are (3, 1)
and (3, 6).

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