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?

The distance between the origin and the final point of the ant is 15 units

What 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 A

Distance 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 plane

Given 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 up

So , 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 up

So , 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 up

So , 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 respectively

Initial point = A ( 0 , 0 )

Final point = D ( 9 , 12 )

Substituting the values in the equation , we get

Distance D = √ ( ( 9 – 0 )² + ( 12 – 0 )² )

Distance D = √ ( 81 ) + ( 144 )

Distance D = √225

Distance D = 15 units

Therefore , the value of Distance D is 15 units

Hence ,

The distance between the origin and the final point of the ant is 15 units

To learn more about distance between two points click :

distancebetween theoriginand the finalpointof the ant is 15 unitsWhat is the distance between two points?pointsbe A ( x₁ , y₁ ) and B ( x₂ , y₂ )distancefrom A to B is the same as the distance from B to ADistancebetween twopointsis thelengthof the line segment that connects the twopointsin a plane.distancebetween the twopointsis usually given by D = √( ( x₂ – x₁ )² + ( y₂ – y₁ )²)distancebetween any twopointson a coordinate plane or x-y planepointof the any be A ( x₁ , y₁ ) = A ( 0 , 0 )pointis = B ( x₂ , y₂ )pointis = C ( x₃ , y₃ )pointis = D ( x₄ , y₄ )distancefrom theoriginand the finalpointD of the ant is given by thedistanceformula ,pointsare A and D respectivelypoint= A ( 0 , 0 )point= D ( 9 , 12 )valuesin theequation, we getDistanceD = √ ( ( 9 – 0 )² + ( 12 – 0 )² )DistanceD = √ ( 81 ) + ( 144 )DistanceD = √225DistanceD = 15 unitsvalueofDistanceD is 15 unitsdistancebetween theoriginand the finalpointof the ant is 15 unitsdistancebetween twopointsclick :