Line segment AB¯¯¯¯¯¯¯¯ has endpoints A(−2,6) and B(4,−6). What are the coordinates of the point that partitions BA¯¯¯¯¯¯¯¯ according to the part-to-part ratio 2:4? Enter your answer as an ordered pair, formatted like this: (42, 53)
Since you say BA, I assume that the point P is 4/6 of the way from A to B?
P = A + 2/3 (B-A)
so ,
x = -2 + 2/3 (4+2) = -2 + 4 = 2
y = -2
So, P = (2,-2)
thank you!!:)
(2, -2) is wrong I took the test
Well, let's turn this serious math problem into a fun circus act! So, the part-to-part ratio is 2:4, which means it can be simplified to 1:2.
To find the point that partitions the line segment AB¯¯¯¯¯¯¯¯ according to this ratio, we need to divide the distance between A and B into two parts. Imagine a little circus clown hopping along the line, splitting it into two sections.
The distance between A and B in the x-direction is 4 - (-2) = 6, and the distance in the y-direction is -6 - 6 = -12. Now, let's divide these distances into two parts according to the ratio 1:2.
So, the x-coordinate of the partition point will be -2 + (1/3) * 6 = 0, and the y-coordinate will be 6 + (1/3) * -12 = 2.
So, the coordinates of the point that partitions line segment AB¯¯¯¯¯¯¯¯ according to the ratio 2:4 (or 1:2) will be (0, 2).
Let the circus act begin! 🤡
To find the coordinates of the point that partitions the line segment AB into a 2:4 ratio, we first need to determine the total distance of the line segment AB. We can use the distance formula to find the distance between points A and B.
The distance formula is given by:
d = √[(x₂ - x₁)² + (y₂ - y₁)²]
Let's calculate the distance between A(-2, 6) and B(4, -6):
d = √[(4 - (-2))² + (-6 - 6)²]
= √[(6)² + (-12)²]
= √[36 + 144]
= √180
= 6√5
So, the total distance of line segment AB is 6√5.
Next, we want to find the coordinates of the point that partitions AB into a 2:4 ratio.
To find the coordinates, we can use the section formula, which states that if we divide a line segment into parts a:b, then the coordinates of the partition point P(x,y) with ratio a:b are given by:
P(x, y) = ((b*x₁ + a*x₂)/(a+b), (b*y₁ + a*y₂)/(a+b))
Plugging in the given values for the endpoints A(-2, 6) and B(4, -6), and the ratios 2:4, we get:
P(x, y) = ((4*(-2) + 2*4)/(2+4), (4*6 + 2*(-6))/(2+4))
= ((-8 + 8)/6, (24 - 12)/6)
= (0/6, 12/6)
= (0, 2)
Therefore, the coordinates of the point that partitions line segment AB into a 2:4 ratio are (0, 2).