Question

If two points known on the line AB in the coordinate plane is (7,15) and (18,42), calculate the following..

A) the slope of the line AB

B) The length of the line AB

Answer 1

• Slope = 27/11
• AB = 29.15 u

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 = ( y_2-y_1)/(x_2-x_(1))`

• Plug in the respective values ,

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

Hence the length of AB is 29.15 units .