Question

1. line segment ab has endpoints at a(-9, 3) and b(1, 8).

we want to find the coordinates of point p so that p partitions ab into a part - to - whole ratio of 1:5.
c. what are the coordinates of point p?

Explanation:

Step1: Recall the section formula for part - to - whole ratio

If a point \(P(x,y)\) divides the line segment joining \(A(x_1,y_1)\) and \(B(x_2,y_2)\) in the part - to - whole ratio \(m:n\), then \(x=x_1+\frac{m}{n}(x_2 - x_1)\) and \(y=y_1+\frac{m}{n}(y_2 - y_1)\). Here, \(x_1=-9,y_1 = 3,x_2=1,y_2 = 8,m = 1,n = 5\).

Step2: Calculate the \(x\) - coordinate of \(P\)

Substitute the values into the \(x\) - coordinate formula:

$$
LATEXBLOCK0
$$

Step3: Calculate the \(y\) - coordinate of \(P\)

Substitute the values into the \(y\) - coordinate formula:

$$
LATEXBLOCK1
$$

Answer:

The coordinates of point \(P\) are \((-7,4)\)