Points A (-10,-6) and B (6,2) are the endpoints of AB. What are the coordinates of point C on AB such that AC is 3/4 the length of AB?
a. (0,-1)
b. (2,0)
c. (-2,-2)
d. (4,1)
B.) (2, 0)
first u find how long AB is which is (16, 8) in length.... 10+6 = 16 and 6+2 = 8.
3/4 * 16 = 12
3/4 * 8 = 6
so starting on point A add (12, 6) to (-10,-6) you will get (2,0) because 12-10=2; 6-6=0
YOU are correct.
Well, finding the coordinates of point C isn't as complex as figuring out why the word "abbreviation" is so long... but I'll give it a shot!
To solve this problem, we first need to calculate the length of AB. The distance formula comes to the rescue here, which is as handy as a pocket on a shirt!
The formula for finding the distance between two points (x₁, y₁) and (x₂, y₂) is:
d = √[(x₂ - x₁)² + (y₂ - y₁)²]
For AB, we plug in the values:
AB = √[(6 - (-10))² + (2 - (-6))²]
= √[16² + 8²]
= √[256 + 64]
= √320
= 4√5
To find point C, we need to locate a point that divides AB into a 3:4 ratio. So, the distance from A to C would be 3/7 times the length of AB, and the distance from C to B would be 4/7 times the length of AB.
To find the coordinates of C, we can use the midpoint formula, which states that the coordinates of the midpoint between two points (x₁, y₁) and (x₂, y₂) are:
(x₁ + x₂)/2, (y₁ + y₂)/2
Plugging in the values, the x-coordinate of C would be:
x = (-10 + (4/7) * 16)/2
= (-10 + 64/7)/2
= (-70 + 64/7)/2
= -6/7
Similarly, the y-coordinate of C would be:
y = (-6 + (4/7) * 8)/2
= (-6 + 32/7)/2
= (-42 + 32/7)/2
= -10/7
Therefore, the coordinates of point C are (-6/7, -10/7). But since none of the answer choices match this value, I guess you could say that the point C is as elusive as finding a cat with opposable thumbs!
To solve this problem, we need to find the coordinates of point C, which lies on the line segment AB and divides it into two parts, such that the length of AC is 3/4 the length of AB.
First, let's find the length of AB using the distance formula:
Distance formula: √[(x₂ - x₁)² + (y₂ - y₁)²]
Coordinates of A: (-10, -6)
Coordinates of B: (6, 2)
Length AB = √[(6 - (-10))² + (2 - (-6))²]
= √[16² + 8²]
= √(256 + 64)
= √320
= 8√5
Now, if AC is 3/4 the length of AB, we can find the length of AC:
Length AC = (3/4) * Length AB
= (3/4) * 8√5
= 6√5
To find the coordinates of point C, we can use the midpoint formula, since C is the midpoint of AB:
Midpoint formula: [((x₁ + x₂)/2), ((y₁ + y₂)/2)]
Using the given coordinates of A and B:
Coordinates of C = [((-10 + 6)/2), ((-6 + 2)/2)]
= [(-4/2), (-4/2)]
= (-2, -2)
Therefore, the coordinates of point C are (-2, -2). Hence, the correct option is c. (-2, -2).