Question

use for questions 1 through 2 : Given line segments AB with endpoints A(-1,7) and B(11,-1)
1) find the length of AB


2)find the midpoint of AB

Answer 1

Question :-

Given line segment AB with endpoints A(-1,7) and B(11,-1).

To find :-

• Length of AB
• Midpoint of AB

Solution :-

(i) To find the length of AB, we measure the distance between these points, using the distance formula.

$distance \: formula = \sqrt{ ({x}_{2} - {x}_{1})^2 + ( {y}_{2} - {y}_{1} )^2 }$

Here,

• x2 = 11
• x1 = -1
• y1 = 7
• y2 = -1

substituting values in the formula,

= √(11-(-1)^2 + (-1-7)^2

= √(11+1)^2 + (-1-7)^2

= √(12)^2+(-8)^2

= √144-64

= √80 sq. units.

____________________________

(ii) Using midpoint formula,

$( \frac{x1 + x2}{2},\frac{y1 + y2}{2} )$

substituting values in the formula,

= (-1+11)/2 , (7+(-1)/2

= (10)/2 , (6)/2

= 5,3

•°• (5,3) is the required point.

Answer 2

• $\underline\mathcal\blue{To\:find...}$

✰✰ length of AB...

✰✰ midpoint of AB...

• $\underline\mathcal\blue{Given...}$

✰✰ A = ( -1, 7 )

✰✰ B = ( 11, -1 )

• $\underline\mathcal\blue{SoLution...}$

We measure the distance between A and B points to find the length of AB by using distance formula...

$\:distance \: formula \: = \: \sqrt{( x_{2} - x_{1}) ^{2} + (y_{2} - x_{1}} ) ^{2}$

x2 = 11

x1 = -1

y2 = -1

y1 = 7

• substituting values in the formula...

√ ( 11 - ( -1 ) )² + ( -1 -7 ) ²

√ 180 sq. units...

• using midpoint formula...

$\dfrac{x1 + x2}{2} , \dfrac{y1 + y2}{2}$

• substituting values in the formula...

$\dfrac{-1 + 11}{2} , \dfrac{7 + (-1)}{2}$

• ===> 5 , 3