Question

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

Answer 1

a)
`y = (3)/(4) x + 3`

The equation of the straight line CD is
`y = (3)/(4) x + 3`

Explanation:

Step(i):-

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

Slope of the line

`m = (y_(2) - y_(1) )/(x_(2) - x_(1) ) = (3-0)/(0-(-4)) = (3)/(4)`

Slope of the line
`m = (3)/(4)`

Step(ii):-

The equation of the straight line passing through the point ( -4,0) and having slope
`m = (3)/(4)`

y - y₁ = m(x-x₁)

`y -0 = (3)/(4) ( x- (-4))`

`y = (3)/(4) x + 3`

The equation of the straight line AB is
`y = (3)/(4) x + 3`

Step(iii):-

CD is parallel to the line AB

The equation of the straight line AB is
`y = (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 = (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=(y_2-y_1)/(x_2-x_1)`

`m=(3-0)/(0-(-4))`

`m=(3)/(4)`

The slope of line AB is
`(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 =
`(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
`(3)/(4)`, it means the line must be of the form

`y=(3)/(4)x+b`

Coefficient of x is
`(3)/(4)` only in option a.

Therefore, the correct option is a.