Question

The endpoint coordinates of AB are A(2, -10) & B(12, 5). Find the coordinates of the point that is 2/5 from A to B.

Answer 1

Answer:
`\large \boldsymbol {\sf 2√(13) \approx7,2}`

Explanation:

• Find the distance between points A and B by the formula:

• 
  `\large \boldsymbol {\sf D=√((x_1-x_2)^2+(y_1+y_2)^2) }`

• 
  `\large \boldsymbol{} \sf D=√((2-12)^2+(-10-5)^2) =√(100+225) =\boldsymbol {√(325)=5√(13) }`

• By the condition we are told to find 2/5 the distance between points A and B

• 
  `\sf \large \boldsymbol {} (2)/(5) \cdot D=5√(13) \cdot (2)/(5) =\boxed{\sf 2√(13)}`

• We can also find the distance between them through the Pythagorean theorem we will complete a right triangle

• AB²=AC²+BC²

• AB=√AC²+BC²

• Where AC=10 ; BC=15

• AB=
  `\boldsymbol {\sf √(15^2+10^2)=√(325)=5√(13) }`

• Then 2/5* AB=2
  `√(13)`