Question

A rectangle is drawn on a coordinate grid. The equation for one side of the rectangle is 2x – 5y = 9. Which could be the equation of another side of the rectangle?

Answer 1

Answer:

$25x+10y+18=0$

Step-by-step explanation:

We are given that a rectangle in which the equation of one side is given by

$2x-5y=9$

We have to find the equation of another side of the rectangle.

We know that the adjacent sides of rectangle are perpendicular to each other.

Differentiate the given equation w.r.t.x

$2-5\frac{dy}{dx}=0$   ($\frac{dx^n}{dx}=nx^{n-1}$)

$5\frac{dy}{dx}=2$

$\frac{dy}{dx}=\frac{2}{5}$

Slope of the given side=$m_1=\frac{2}{5}$

When two lines are perpendicular then

Slope of one line=$-\frac{1}{Slope\;of\;another\;line}$

Slope of another side=$-\frac{5}{2}$

Substitute x=0 in given equation

$2(0)-5y=9$

$-5y=9$

$y=-\frac{9}{5}$

The equation of given side is passing through the point ($0,-\frac{9}{5})$.

The equation of line passing through the point $(x_1,y_1)$ with slope m is given by

$y-y_1=m(x-x_1)$

Substitute the values then we get

$y+\frac{9}{5}=-\frac{5}{2}(x-0)=-\frac{5}{2}x$

$y=-\frac{5}{2}x-\frac{9}{5}$

$y=\frac{-25x-18}{10}$

$10y=-25x-18$

$25x+10y+18=0$

Hence, the equation of another side of rectangle is given by

$25x+10y+18=0$

Answer 2

Answer:

y=2/5x-9

I just answered this and got it right.

Step-by-step explanation: