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

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 .