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Luda [366]
3 years ago
14

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 le

ngth of the line AB
Mathematics
1 answer:
posledela3 years ago
3 0

Answer:

Slope = 27/11

AB = 29.15 u

Step-by-step explanation:

<u>Given </u><u>:</u><u>-</u><u> </u>

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

<u>To </u><u>Find </u><u>:</u><u>-</u><u> </u>

  • 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 }}

<u>Hence </u><u>the</u><u> </u><u>slope </u><u>of</u><u> the</u><u> line</u><u> </u><u>is </u><u>2</u><u>7</u><u>/</u><u>1</u><u>1</u><u> </u><u>.</u>

\rule{200}2

<u>Finding </u><u>the</u><u> </u><u>length</u><u> </u><u>of </u><u>AB </u><u>:</u><u>-</u>

  • 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 }

<u>Hence</u><u> the</u><u> </u><u>length</u><u> of</u><u> </u><u>AB </u><u>is </u><u>2</u><u>9</u><u>.</u><u>1</u><u>5</u><u> </u><u>units </u><u>.</u>

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