Question

Find the coordinates of the point 7/10 of the way from point A (-4, -7) to B (12, 4) with explantation

Answer 1

We have to find the point that is at 7/10 of the way from point A (-4, -7) to B (12, 4).

We can represent this problem as:

We can find the coordinates of the point C knowing that the proportion of the segment (7/10) applies for the horizontal distance and the vertical distance.

Then, the x-coordinate of C will be the coordinate of A plus 7/10 of the horizontal distance between B and A (in other words, the difference between teh x-coordinates of B and A).

We then can calculate it as:

`\begin{gathered} x_C=x_A+(7)/(10)(x_B-x_A) \\ \\ x_C=-4+(7)/(10)(12-(-4)) \\ \\ x_C=-4+(7)/(10)(16) \\ \\ x_C=-4+11.2 \\ \\ x_C=7.2 \end{gathered}`

We can apply the same principle for the y-coordinate:

`\begin{gathered} y_C=y_A+(7)/(10)(y_B-y_A) \\ \\ y_C=-7+(7)/(10)(4-(-7)) \\ \\ y_C=-7+(7)/(10)(11) \\ \\ y_C=-7+7.7 \\ \\ y_C=0.7 \end{gathered}`

Answer: the point at 7/10 of the way between A and B has the coordinates (7.2, 0.7)