Question

what are the coordinates of point b in the diagram?
a. (3.25, -2.5)
b. (4, -5)
c. (1, 3)
d. (2.5, 0)

Explanation:

Step1: Analyze the x - coordinate change

From point \(A=(1,5)\) to point \(C=(1.75,2.5)\), the change in \(x\) - coordinate is \(1.75 - 1=0.75\). Each segment (assuming equal - length segments) has an \(x\) - coordinate change. From \(A\) to \(C\) is one segment. If we consider the total number of segments from \(A\) to \(B\) (assuming 4 equal - length segments from \(A\) to \(B\) as per the diagram's visual equal - division), the total change in \(x\) from \(A\) to \(B\) is \(0.75\times4 = 3\). So the \(x\) - coordinate of \(B\) is \(1+3 = 4\).

Step2: Analyze the y - coordinate change

From point \(A=(1,5)\) to point \(C=(1.75,2.5)\), the change in \(y\) - coordinate is \(2.5 - 5=-2.5\). Each segment has a \(y\) - coordinate change of \(- 2.5\). For 4 segments from \(A\) to \(B\), the total change in \(y\) is \(-2.5\times4=-10\). But wait, another way: if we assume a linear relationship. Let's use the concept of equal - division. If we consider the vector from \(A\) to \(C\) as \(\vec{v}=(\Delta x,\Delta y)=(0.75, - 2.5)\). If from \(A\) to \(B\) is 4 times the vector from \(A\) to \(C\) (visually from the diagram with 4 equal - length parts from \(A\) to \(B\) passing through \(C\) and two other points). The \(y\) - coordinate of \(B\): starting from \(y = 5\), and with a change of \(-2.5\) per segment. After 4 segments, \(y=5+(-2.5)\times4=5 - 10=-5\).

Answer:

B. \((4,-5)\)