Question

a = (1, 5)
c = (1.75, 2.5)
b = (?)
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: Find the pattern of coordinate change

From \(A=(1,5)\) to \(C=(1.75,2.5)\), the \(x\) - coordinate changes by \(1.75 - 1=0.75\), and the \(y\) - coordinate changes by \(2.5 - 5=- 2.5\).

Step2: Calculate the coordinates of \(B\)

Since \(C\) is the first - quarter point from \(A\) to \(B\), from \(A\) to \(B\), the \(x\) - coordinate change is \(0.75\times4 = 3\), and the \(y\) - coordinate change is \(-2.5\times4=-10\).
The \(x\) - coordinate of \(B\) is \(1 + 3=4\), and the \(y\) - coordinate of \(B\) is \(5+( - 10)=-5\).

Answer:

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