if coordinates of one diagonal of rectangle are (2, 1) and (4, 3) and other two vertices lie on the line 2x - y = k then the value of k will be

Question

Question

Answer 1

Formula used:

The midpoint of two-point (x1, y1) and (x2, y2) is given by

$(\frac{x_{1} + x_{2}}{2}, \frac{y_{1} + y_{2}}{2})$

Calculation:

Given that, point (2, 1) and (4, 3) are opposite vertices of rectangle

F1 Sachin mishra Shraddha 06.10.2021 D4

The mid-point of A(2, 1) and C(4, 3)

= $(\frac{2 + 4}{2}, \frac{1 + 3}{2})$ = (3, 2)

We know that the intersecting point of the diagonal of a rectangle is the same or at the midpoint.

Therefore, the point (3, 2) will satisfy the equation 2x - y = k

⇒ 2(3) - 2 = k

⇒ k = 4

Hence, option 3 is correct.

Additional Information1. Equation of line of slope m passing through the point (x₁, y₁) is

(y - y₁) = m(x - x₁)

2. Equation of line passing through (x1, y1) and (x2, y2) is

$(y - y_{1}) = \frac{y_{2} - y_{1}}{x_{2} - x_{1}} (x - x_{1})$