Answer:
In this problem, there is multiple choice for every question. The trick is to exclude the answer that unlikely true.
To solve this easier, you need to find the distance of AB first. After that try to match the answer coordinate with the midpoint of AB.
1. Answer: Point C(-3.6, -3.4) divides AB in the ratio 2:3
A (-2,-1) and B(-6, -7)The distance between A and B would be:
x= x2-x1 = -6 - (-2)= -4
y= y2-y1 = -7 - (-1)= -6
Since both x and y coordinate of A and B is minus, let's try answer with x and y minus value.
Point C(-3.6, -3.4) divides AB in the ratio 2:3
x3= x1 + AB ratio* AB distance
x3= -2 + (2/2+3)*(-4)= -3.6
y3= y1 + AB ratio* AB distance
y3= -1 + (2/2+3)*(-6)= -1 - 12/5= -3.4
2. Point C(0, 1) divides AB in the ratio 4:7
A(4,-3) and B(-7,8)
The distance between A and B would be:
x= x2-x1 = -7 - (4)= -11
y= y2-y1 = 8 - (-3)= 11
Since both x and y distance is 11, let's try answer with total ratio 11
Point C(0, 1) divides AB in the ratio 4:7
x3= x1 + AB ratio* AB distance
x3= 4 + (4/4+7)*(-11)= 4- 4=0
y3= y1 + AB ratio* AB distance
y3= -3 + (4/4+7)*(11)= -3 +4= 1
3. Answer: Point C(8, 9) divides AB in the ratio 5:3
A(3,4) and B(11,12)The distance between A and B would be:
x= x2-x1 = 11 - (3)= 8
y= y2-y1 = 12 - (4)= 8
Since both x and y distance is 8, let's try answer with the total ratio 8. Both of x and y also plus, so focus on coordinate with both x and y plus too.
Point C(3.5, -2.5) divides AB in the ratio 1:7-----> total ratio 8,y minus
Point C(-2, 5) divides AB in the ratio 2:6 -----> total ratio 8, x minus
Point C(8, 9) divides AB in the ratio 5:3 -----> total ratio 8, both x and y plus
x3= x1 + AB ratio* AB distance
x3= 3 + (5/5+3)*(8)= 3+ 5=8
y3= y1 + AB ratio* AB distance
y3= 4 + (5/5+3)*(8)= 4 +5= 9
4. Point C(-2, 5) divides AB in the ratio 2:6
A(-5,2)and B(7, 14)
The distance between A and B would be:
x= x2-x1 = 7 - (-5)= 12
y= y2-y1 = 14 - (2)= 12
Since both x and y distance is 12, it will be hard to use it since 12 has many factors. Both y coordinate is plus, so focus on coordinate with y more than x and plus.
Point C(4, 1.6) divides AB in the ratio 3:2 -----> x more than y
Point C(-2, 5) divides AB in the ratio 2:6 -------> y plus, y more than xx3= x1 + AB ratio* AB distance
x3= -5 + (2/2+6)*(12)= -5+ 3=-2
y3= y1 + AB ratio* AB distance
y3= 2 + (2/2+6)*(12)= 2 +3= 5
Explanation: