Starting at the origin of a coordinate graph, an ant crawls 1 unit to the right, 2 units up, 3 units to the right, 4 units up, 5 units to the right, and 6 units up. How far from the origin is the ant currently located?
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The distance between the origin and the final point of the ant is 15 unitsWhat is the distance between two points?Let the two points be A ( x₁ , y₁ ) and B ( x₂ , y₂ )The distance from A to B is the same as the distance from B to ADistance between two points is the length of the line segment that connects the two points in a plane.The formula to find the distance between the two points is usually given by D = √( ( x₂ – x₁ )² + ( y₂ – y₁ )²)This formula is used to find the distance between any two points on a coordinate plane or x-y planeGiven data ,Let the initial point of the any be A ( x₁ , y₁ ) = A ( 0 , 0 )Now , the ant crawls 1 unit to the right and 2 units upSo , the coordinates of ant at second point is = B ( x₂ , y₂ )B ( x₂ , y₂ ) = B ( 0 + 1 , 0 + 2 )B ( x₂ , y₂ ) = B ( 1 , 2 )Now , the ant crawls 3 unit to the right and 4 units upSo , the coordinates of ant at second point is = C ( x₃ , y₃ )C ( x₃ , y₃ ) = C ( 1 + 3 , 2 + 4 )C ( x₃ , y₃ ) = C ( 4 , 6 )Now , the ant crawls 5 unit to the right and 6 units upSo , the coordinates of ant at second point is = D ( x₄ , y₄ )D ( x₄ , y₄ ) = D ( 4 + 5 , 5 + 6 )D ( x₄ , y₄ ) = D ( 9 , 12 )Now , the distance from the origin and the final point D of the ant is given by the distance formula ,D = √( ( x₂ – x₁ )² + ( y₂ – y₁ )²)where the initial and final points are A and D respectivelyInitial point = A ( 0 , 0 )Final point = D ( 9 , 12 )Substituting the values in the equation , we getDistance D = √ ( ( 9 – 0 )² + ( 12 – 0 )² )Distance D = √ ( 81 ) + ( 144 )Distance D = √225Distance D = 15 unitsTherefore , the value of Distance D is 15 unitsHence ,The distance between the origin and the final point of the ant is 15 unitsTo learn more about distance between two points click :https://brainly.com/question/12661159#SPJ1