Question

1
select the correct answer.
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 \(\Delta x=1.75 - 1=0.75\), and the change in \(y\) - coordinate is \(\Delta y=2.5 - 5=- 2.5\).

Step2: Calculate the total change from \(A\) to \(B\)

Since there are 4 equal - length segments from \(A\) to \(B\) (counting the segments between \(A\) and \(C\) as one of them). The total change in \(x\) from \(A\) to \(B\) is \(4\times0.75 = 3\). The total change in \(y\) from \(A\) to \(B\) is \(4\times(-2.5)=-10\).

Step3: Find the coordinates of \(B\)

Using the formula \((x,y)=(x_A+\Delta x_{total},y_A+\Delta y_{total})\). Here \(x_A = 1\), \(y_A = 5\), \(\Delta x_{total}=3\), \(\Delta y_{total}=-10\). So \(x=1 + 3=4\), \(y=5-10=-5\)

Answer:

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