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Suppose line segment XY has one endpoint at X(0,0).

Question 1- Is (3,4) is the midpoint of line segment XY, what are the coordinates of point y?

Question 2- What are the coordinates of Y if (3,4) is 1/3 of the way from X to Y?

Respuesta :

xero099

Answer:

1) The coordinates of point Y are [tex](6,8)[/tex], 2) The coordinates of point Y are [tex](9,12)[/tex].

Step-by-step explanation:

1) We know that [tex]X = (0, 0)[/tex] and [tex]M = (3, 4)[/tex], being the latter one the midpoint of line segment XY. Vectorially, the location of point Y is determined by the following expression:

[tex]Y = X + 2\cdot M[/tex]

Now we solve the expression above:

[tex]Y = (0,0)+2\cdot (3,4)[/tex]

[tex]Y =(0,0) +(6,8)[/tex]

[tex]Y = (0+6,0+8)[/tex]

[tex]Y = (6,8)[/tex]

The coordinates of point Y are [tex](6,8)[/tex].

2) We know that [tex]X = (0, 0)[/tex] and [tex]M = (3, 4)[/tex], being the latter one a third of the way of line segment XY.

Vectorially, the location of point Y is determined by the following expression:

[tex]Y = X + 3\cdot M[/tex]

Now we solve the expression above:

[tex]Y = (0,0)+3\cdot (3,4)[/tex]

[tex]Y =(0,0) +(9,12)[/tex]

[tex]Y = (0+9,0+12)[/tex]

[tex]Y = (9,12)[/tex]

The coordinates of point Y are [tex](9,12)[/tex].

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