Question

select the correct answer.
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 x - coordinate change

The x - coordinate of A is 1 and of C is 1.75. The difference between the x - coordinates of C and A is \(1.75 - 1=0.75\). There are 3 equal - length segments from A to C. So the change in x - coordinate for each segment is \(\frac{1.75 - 1}{3}=0.25\).

Step2: Find the x - coordinate of B

Since there are 4 segments from A to B, the change in x - coordinate from A to B is \(0.25\times4 = 1\). The x - coordinate of A is 1, so the x - coordinate of B is \(1+0.25\times4=3.25\).

Step3: Find the pattern of y - coordinate change

The y - coordinate of A is 5 and of C is 2.5. The difference between the y - coordinates of C and A is \(2.5 - 5=- 2.5\). The change in y - coordinate for each segment is \(\frac{2.5 - 5}{3}=-\frac{2.5}{3}\).

Step4: Find the y - coordinate of B

The change in y - coordinate from A to B is \(-\frac{2.5}{3}\times4=- 2.5\). The y - coordinate of A is 5, so the y - coordinate of B is \(5+( - 2.5\times4\div3)=5 - 7.5=-2.5\).

Answer:

A. \((3.25,-2.5)\)