Answer:
Assuming that 34 is supposed to read 3/4, the point (not A) is located a distance of 7.65 on the line between A and B. [Maybe 97.65,8.2)]?
Step-by-step explanation:
I'll assume that 34 is supposed to read 3/4 and that there is a third point, I'll call C. The point in question is not point A, since it has already been defined as (5,4). Points A(5,4) and B(10,12) form a straight line with a slope of 8/5, to yield the equation y = (8/5)x + b, where b is the y intercept. We can calculate b by using one of the points, A, in this example:
4 = (8/5)(5) + b
4 = 8 + b
b = -4
The equation is y = (8/5)x - 4
By solving this equation for y=0, we find that i croses the x axis at x=2.5. Thus, point A is (2.5,0)
To find the point that is 3/4 the distance from A, we can make a right triangle from point B down to the x axis, to a point I'll call H. The length of this verticle line, BH, is 12. The length of AH is 9.5 (12-2.5).
Use the quadratic formula to find the hypotenuse, which is line AB. I find 15.31, which is a bit odd, so there may be a mistake here. But knowing the length of AB would now allow calculation of the midpoint.
