Question

Segment AB was partitioned at a 1:3 ratio at point C. If point A is located at (3, 5) and point C is located at (6, 10). What are the coordinates of point B?
Question 2 options:

(12, 15)


(6, 10)


(9, 12)


(3, 1)

Question 3 (1 point)
Point G is located at (3, 2) and point H is located at (15, 8). What are the coordinates of the point that partitions the directed line segment GH in a 4:1 ratio?

Question 3 options:
Question 4 (1 point)
What are the coordinates of the midpoint of the line segment with endpoints B (9, -8) and C (2, -5).

Question 4 options:
Question 5 (1 point)
A directed line segment is a line that is divided into partitions.

Question 5 options:
True
False

Answer 1

Question 2:

We have that point C(6,10) partitions A(3,5) and B(a,b) in the ratio m:n=1:3

We use the section formula:

$(x,y)=(\frac{mx_2+nx_1}{m+n}, \frac{my_2+ny_1}{m+n})$

We substitute the values to get:

$(6,10)=(\frac{1*a+3*3}{1+3}, \frac{1*b+3*5}{1+3})$

We simplify to get:

$(6,10)=(\frac{a+9}{4}, \frac{b+15}{4})$

This implies that:

$(6=\frac{a+9}{4},10= \frac{b+15}{4})$

$(24=a+9,40= b+15)$

$(a=15,b=25)$

The  coordinates of B are (15,25)

Question 3:

This time we have G(3,2) and H(15,8), and we want to find C(x,y) that partitions GH in a m;n=4:1 ratio:

We apply the section formula to get:

$(x,y)=(\frac{4*15+1*3}{4+1}, \frac{4*8+1*2}{4+1})$

$(x,y)=(\frac{60+3}{5}, \frac{32+2}{5})$

$(x,y)=(\frac{63}{5}, \frac{34}{5})$

Question 4

We want to find the coordinates of the midpoint of  the line segment with endpoints B (9, -8) and C (2, -5),

The midpoint is given by:

$(x,y)=(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})$

We substitute the endpoints to obtain:

$(x,y)=(\frac{9+2}{2}, \frac{-1+-5}{2})$

This simplifies to:

$(x,y)=(\frac{11}{2}, \frac{-6}{2})$

The midpoint is:

$(5\frac{1}{2}, -3)$

Question 5

A directed line segment has length and direction. That means there is a beginning point and an endpoint.

Partitions can occur on a directed line segments. This does not mean that all directed line segment must be partitioned.

Ans: False