Question

1. A line segment has endpoints of Y(2,-3) and Z(-6,-1).

Answer 1

The answers will be :

a. The length of the line segment will be equal to 8.24 units.

b. The midpoint of the line segment will be ( -2 , -2 ).

c. The equation of line passing through points Y and Z will be 4y + x - 10 = 0

What is slope of a line segment ?

The ratio of the difference in y-coordinates over the equivalent x-coordinates between two different locations on a line.

It is given that a line segment has endpoints of Y(2,-3) and Z(-6,-1).

Let's solve the given parts based on the above data.

a.

The length of the line segment will be given by :

YZ = $\sqrt({x_{2} - x_{1})^2 + (y_{2}- y_{1})^2}$

YZ = √ [( -6 -(2)]^2 + [ -1 - (-3)]^2}

YZ = √ (-8)² + 2²)

YZ = √68

YZ = 8.24 units

b.

The midpoint (say M) of the line segment will be given by :

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

M = [(2-6)/2 , (-3-1)/2]

M = ( -2 , -2 )

c.

And the equation of line passing through points Y and Z will be :

$y_{2} - y_{1}$ = m ( $x_{2} - x_{1}$ )

Let's calculate value of slope (m) firstly which will be :

m =($y_{2} - y_{1}$) / ( $x_{2} - x_{1}$ )

m = ( -1 + 3 ) / (-6 - 2)

m = 2 / -8

m = -1 / 4

or

m = -0.25

Using the value of slope (m) : we get the equation of line as :

$y - y_{1}$ = - 0.25 ( $x - x_{1}$ )

or

(y + 3) = - 0.25 ( x - 2)

y + 3 = -0.25 x + 0.50

or

y + 0.25 x - 2.5 = 0

If we multiply by 4 throughout the equation ; then the equation of line can also be written as :

4y + x - 10 = 0

Therefore the answers will be :

a. The length of the line segment will be equal to 8.24 units.

b. The midpoint of the line segment will be ( -2 , -2 ).

c. The equation of line passing through points Y and Z will be 4y + x - 10 = 0

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