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Ber [7]
3 years ago
12

A line segment AB is increased along its length by 25% by producing it to C on the side of B . If A and B have the coordinates (

1 , 2 ) and ( 5 , 6 ) respectively then find the coordinates of C.
Ans : ( 6 , 7 )

*Please show your workings* ​
Mathematics
2 answers:
algol133 years ago
8 0

Answer:

  • C = (6, 7)

Step-by-step explanation:

<u>Coordinates of point B in terms of A and C:</u>

  • x = x₁ + (x₂ - x₁)*a/(a + b)
  • y = y₁ + (y₂ - y₁)*a/(a + b)
  • B(x, y) = (5, 6), A(x₁, y₁) = (1, 2), C(x₂, y₂) = ?

<u>Find the coordinates:</u>

  • 5 = 1 + (x₂ - 1)*4/5  ⇒ 4 = 4/5*(x₂ - 1) ⇒ x₂ - 1 = 5 ⇒ x₂  = 6
  • 6 = 2 + (y₂ - 2)*4/5 ⇒ 4 = 4/5(y₂ - 2) ⇒ y₂ - 2 = 5 ⇒ y₂ = 7
  • C = (6, 7)
kykrilka [37]3 years ago
6 0

Line segment AB goes from point A: (1, 2) to point B: (5, 6)

You increase the length by 25% by finding point C, 25% further away from point A than B is away from A.

How do you find the coordinates of point C?

X coordinate:

What is the distance on the X-axis from X = 1 to X = 5?

5 - 1 = 4

The x-coordinates are 4 apart

What number is 25% higher that 4?

4 × 125% = 5

What X-coordinate is 5 away from 1?

1 + 5 = 6

Point C’s x-coordinate is 6

Y coordinate:

What is the distance on the y-axis from Y = 2 to Y = 6?

6 - 2 = 4

The y-coordinates are 4 apart

What is 25% higher than 4?

Add one-fourth of 4 to the number

4 + (¼×4) = 4 + 1 = 5

What Y-coordinate is 5 away from 2?

2 + 5 = 7

Point C’s y-coordinate is 7

pls giv meh bwainless uwu

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