Question

If two points known on the line A B in the coordinate plane is (7,15) and (18,42), calculate the slope of the line AB and the length of the line AB

Answer 1

Answer:

Slope = 27/11

AB = 29.15 u

Step-by-step explanation:

Given :-

• Two points are given to us .
• The points are A(7,15) and B(18,42)

To Find :-

• The slope of the line .
• The length of line AB .

We can find the slope of the line passing through the points $( x_1,y_1)$ and $( x_2,y_2)$as ,

$\implies m = \dfrac{ y_2-y_1}{x_2-x_{1}}$

• Plug in the respective values ,

$\implies m = \dfrac{ 42-15}{18-7} \\\\\implies \boxed{ m = \dfrac{ 27}{11 }}$

Hence the slope of the line is 27/11 .

$\rule{200}2$

Finding the length of AB :-

• We can find the distance between them by using the Distance Formula .

$\implies Distance =\sqrt{ (x_2-x_1)^2+(y_2-y_1)^2} \\\\\implies Distance =\sqrt{ (18-7)^2+(42-15)^2 } \\\\\implies Distance =\sqrt{ 11^2 + 27^2 } \\\\\implies Distance =\sqrt{ 121 + 729 } \\\\\implies Distance = \sqrt{ 850} \\\\\implies \boxed{ Distance = 29.15 \ units }$

Hence the length of AB is 29.15 units .