Question

What are the coordinates of the point between A to B 7/10ths of the way

Answer 1

Coordinates are (5.4, 2.1)

Explanation:

The two points are A(-3, -7) and B(9, 6)

The x distance from A to B = 9 - (-3) = 9 + 3 = 12

The y distance from A to B = 6 - (-7) = 6 + 7 = 13

7/10 of the x-distance = 7/10 x 12 = 84/10 = 8.4

7/10 of the y-distance = 7/10 x 13 = 91/10 = 9.1

For this point(let's call it C) to find absolute coordinates we have to add the x, y coordinates of point A

x-coordinate absolute value = -3 + 8.4 = 5.4

y-coordinate absolute value = -7 + 9.1 = 2.1

So the coordinates of the point C are (5.4, 2.1)

To check if this point is 7/10 of AB segment

Use the distance formula to find the distance between two points A(x1, y1) and B(x2, y2)

`d = \sqrt {(x_(2) - x_(1))^2 + (y_(2) - y_(1))^2}`

Using this formula length AB = 17.7

Length AC = 12.384264 ≅ 12.4

12.4/17.7 = 0.70056 ≅ 0.7 = 7/10

Thus verified