Question

If line segment RU is considered the base of parallelogram RSTU, what is the corresponding height of the parallelogram?

Answer 1

vertices: (1,1) ,(4,5) , (10,4) , (7,0)
we can use the cross product
| RU X RS | / distance(1,1,4,5)

b)5.4 units

Answer 2

The corresponding height of the parallelogram is
`(27)/(5)` units

Solution-

Hint- The perpendicular distance between the point S and the straight line RU is the length of the height of the parallelogram.

Equation of RU-

Applying two point formula between (4, 5), (1, 1)

`\Rightarrow (y-y_1)/(y_2-y_1)=(x-x_1)/(x_2-x_1)`

`\Rightarrow (y-5)/(1-5)=(x-4)/(1-4)`

`\Rightarrow (y-5)/(-4)=(x-4)/(-3)`

`\Rightarrow (y-5)/(4)=(x-4)/(3)`

`\Rightarrow 3(y-5)=4(x-4)`

`\Rightarrow 3y-15=4x-16`

`\Rightarrow 4x-3y-1=0`

Perpendicular distance between S and RU-

The distance d from a point (x₀, y₀) to the line ax+by+c=0 is

`d=(|ax_0+by_0+c|)/(√(a^2+b^2))`

Distance of (7, 0) from line
`4x-3y-1=0` is,

`d=(|(4)(7)+(-3)(0)+(-1)|)/(√((4)^2+(-3)^2))`

`=(|28-1|)/(√(16+9))`

`=(|27|)/(√(25))`

`=(27)/(5)`