Answer:
The distance between M(7, 8) and N(-3,-8) is 18.87.
Step-by-step explanation:
Solution :
Here's the required formula to find distance:
[tex]\star{\underline{\boxed{\sf{\pink{\sqrt{\Big({x_{2} - x_{1} \Big)}^{2} + {\Big(y_{2} - y_{1} \Big)}^{2}}}}}}}[/tex]
- [tex]\rm{ x_2}[/tex] = -3
- [tex]\rm{ x_1}[/tex] = 7
- [tex]\rm{ y_2}[/tex] = -8
- [tex]\rm{ y_1}[/tex] = 8
Substituting all the given values in the formula to find distance :
[tex]{\implies{\sf{Distance = \sqrt{\Big({x_{2} - x_{1} \Big)}^{2} + {\Big(y_{2} - y_{1} \Big)}^{2}}}}}[/tex]
[tex]{\implies{\sf{Distance = \sqrt{\Big((- 3) -( 7) \Big)^{2} + \Big(( - 8 )-( 8) \Big)^{2}}}}}[/tex]
[tex]{\implies{\sf{Distance = \sqrt{\Big( - 10\Big)^{2} + \Big( - 16\Big)^{2}}}}}[/tex]
[tex]{\implies{\sf{Distance = \sqrt{\Big( - 10 \times - 10\Big) + \Big( - 16 \times - 16\Big)}}}}[/tex]
[tex]{\implies{\sf{Distance = \sqrt{\Big(100\Big) + \Big(256\Big)}}}}[/tex]
[tex]{\implies{\sf{Distance = \sqrt{100+ 256}}}}[/tex]
[tex]{\implies{\sf{Distance = \sqrt{356}}}}[/tex]
[tex]{\implies{\sf{Distance =18.87}}}[/tex]
[tex]\star{\underline{\boxed{\sf{\pink{Distance = 18.87 \: units}}}}}[/tex]
Hence, the distance between M(7, 8) and N(-3,-8) is 18.87.
[tex]\rule{300}{2.5}[/tex]
