Question

Does anyone get this ? if so can u lmk the answer thxxxx:)

Answer 1

Answer:

a)   $y = \frac{3}{4} x + 3$

The equation of the straight line CD is    $y = \frac{3}{4} x + 3$

Step-by-step explanation:

Step(i):-

Given points are A (-4,0) and B( 0,3)

Slope of the line

   $m = \frac{y_{2} - y_{1} }{x_{2} - x_{1} } = \frac{3-0}{0-(-4)} = \frac{3}{4}$

Slope of the line     $m = \frac{3}{4}$

Step(ii):-

The equation of the straight line passing through the point ( -4,0) and having slope    $m = \frac{3}{4}$

y - y₁ = m(x-x₁)

$y -0 = \frac{3}{4} ( x- (-4))$

$y = \frac{3}{4} x + 3$

The equation of the straight line AB is    $y = \frac{3}{4} x + 3$

Step(iii):-

CD is parallel to the line AB

The equation of the straight line AB is    $y = \frac{3}{4} x + 3$

                                     4 y = 3 x + 12

                                    3x - 4y +12 =0

The equation of the Parallel line is   3 x -4y +k=0

Passes through the point ( 0,3)

                                 -12 +k=0

                                      k =12

The equation of the Parallel line is   3 x -4y +12=0

                                                       4 y = 3 x+12

The equation of the straight line CD is    $y = \frac{3}{4} x + 3$

Answer 2

Given:

In parallelogram ABCD, two of its vertices are A(-4,0) and B(0,3).

To find:

The equation that represents a line that contain CD.

Solution:

We have,

A(-4,0) and B(0,3)

Slope of AB is

$m=\dfrac{y_2-y_1}{x_2-x_1}$

$m=\dfrac{3-0}{0-(-4)}$

$m=\dfrac{3}{4}$

The slope of line AB is $\dfrac{3}{4}$.

Opposite sides of a parallelogram are parallel and slopes of parallel lines are equal.

In parallelogram ABCD, AB and CD are opposite sides. So, their slopes must be equal.

Slope of line AB = Slope of line CD = $\dfrac{3}{4}$

The slope intercept form of a line is

$y=mx+b$

Where, m is slope and b is y-intercept.

Slope of line CD is $\dfrac{3}{4}$, it means the line must be of the form

$y=\dfrac{3}{4}x+b$

Coefficient of x is $\dfrac{3}{4}$ only in option a.

Therefore, the correct option is a.