Respuesta :

Answer:

The coordinates of the point at 3/4 of the distance from A to B from A is (-3.5, 1.25)

Step-by-step explanation:

The coordinates of the point A is (-5, -4),

The coordinates of the point B is (-3, 3)

Let the point 3/4 from A to B = P

The coordinates of the point 3/4 from A to B is found as follows;

(-5 + (3/4×(-3 - (-5)), -4 + 3/4×(3 - (-4)) which gives;

The coordinates of the point 3/4 from A to B as P(-3.5, 1.25)

We verify the length from A to B  and from A to P as follows;

The distance l between two points (x₁, y₁) and  (x₂, y₂) is given by the formula;

[tex]\sqrt{\left (y_{2}-y_{1} \right )^{2}+\left (x_{2}-x_{1} \right )^{2}}[/tex]

For AB, we have;

[tex]Length \ of \ segment \ \overline {AB} = \sqrt{\left (3-(-4) \right )^{2}+\left ((-3)-(-5) \right )^{2}}=\sqrt{53} \approx 7.28[/tex]

[tex]Length \ of \ segment \ \overline {AP} = \sqrt{\left (1.25-(-4) \right )^{2}+\left ((-3.5)-(-5) \right )^{2}}= \dfrac{3}{4} \cdot \sqrt{53}[/tex]

Therefore, the point P (-3.5, 1.25) is the point 3/4 distance of A to B from A.

Identifying the distance and applying the fraction, it is found that the coordinates are (-3.5, 1.25).

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  • Point A has horizontal coordinate -5 and vertical coordinate -4, thus, it's coordinates are A(x,y) = A(-5,-4).
  • Point B has horizontal coordinate -3 and vertical coordinate 3, thus, it's coordinates are B(-3,3).

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  • At the x-coordinate, the distance from B to A is of [tex]-3 - (-5) = -3 + 5 = 2[/tex] units.
  • Starting at point A, 3/4 of the way will have a x-coordinate of:

[tex]x = -5 + 2\frac{3}{4} = -5 + \frac{6}{4} = -\frac{20}{4} + \frac{6}{4} = -\frac{14}{4} = -\frac{7}{2} = -3.5[/tex]

  • At the y-coordinate, the distance from B to A is of [tex]3 - (-4) = 3 + 4 = 7[/tex] units.
  • Starting at point A, 3/4 of the way will have a y-coordinate of:

[tex]y = -4 + 7\frac{3}{4} = -4 + \frac{21}{4} = -\frac{16}{4} + \frac{21}{4} = \frac{5}{4} = 1.25[/tex]

The coordinates are (-3.5, 1.25).

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