Answer:
(5.4, 2.7)
Step-by-step explanation:
The coordinates of the point 7/10 of the way from A to B is given by the relation;
(x₁ + m×(x₂ - x₁), y₁ + m×(y₂ - y₁))
Where the coordinate of point A is (-3, -5) and the coordinates of the point B is (9, 6) we have;
x₁ = -3
m = 7/10
x₂ = 9
y₁ = -5
y₂ = 6
Substituting the values into the above equation gives;
-3 + 7/10 × (9 - (-3)), -5 + 7/10 × (6 - (-5)) = (5.4, 2.7)
The coordinate of the point P, 7/10 from A is (5.4, 2.7)
We check the length of the point from A to B to give;
[tex]l = \sqrt{\left (y_{2}-y_{1} \right )^{2}+\left (x_{2}-x_{1} \right )^{2}}[/tex] =
[tex]l_{AB} = \sqrt{\left (6-(-5) \right )^{2}+\left (9-(-5) \right )^{2}} = \sqrt{265}[/tex]
the length of the point from A to B gives
[tex]l_{AB} = \sqrt{\left (2.7-(-5) \right )^{2}+\left (5.4-(-5) \right )^{2}} = \dfrac{7}{10} \times \sqrt{265}[/tex]
The coordinate of the point 7/10 of the way from A to B are (5.4, 2.7).
