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Korvikt [17]
3 years ago
5

The vertices of rectangle ABCD are A(3, 1), B(-5, 1),

Mathematics
1 answer:
OlgaM077 [116]3 years ago
4 0
The answer is (3,-1)
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What is a and b pls answer ASAP I need it !!! Plsss
nlexa [21]

Answer:

The value of a = 5.

the value of b = 6.

Step-by-step explanation:

Given the points on the line

  • (6, 10)
  • (a, 8)
  • (4, b)
  • (2, 2)

Given that all of the points are on the same line and the line represents a linear function.

Thus, the slope between any two points must be the same.

First, determine the slope between (6, 10) and (2, 2)

(x₁, y₁) = (6, 10)

(x₂, y₂) = (2, 2)

Using the formula

Slope = m =  [y₂ - y₁] /  [x₂ - x₁]

               =  [2 - 10] / [2 - 6]

               = -8 / -4  

               = 2

Thus, the slope of the line = m = 2

Determine the value 'a'

(x₁, y₁) = (6, 10)

(x₂, y₂) = (a, 8)

Using the slope formula to determine the value of 'a'

Slope =  [y₂ - y₁] /  [x₂ - x₁]

As the slope between two points is 2.

now substitute slope = 2, (x₁, y₁) = (6, 10) and (x₂, y₂) = (a, 8) in the slope formula

Slope =  [y₂ - y₁] /  [x₂ - x₁]

2 = [8 - 10] / [a - 6]

2(a - 6) = 8 - 10

2a - 12 = -2

2a = -2 + 12

2a = 10

divide both sides by 2

a = 5

Therefore, the value of a = 5.

Determine the value 'b'

(x₁, y₁) = (2, 2)

(x₂, y₂) = (4, b)

Using the slope formula to determine the value of 'b'

Slope =  [y₂ - y₁] /  [x₂ - x₁]

As the slope between two points is 2.

now substitute slope = 2, (x₁, y₁) = (2, 2) and (x₂, y₂) = (4, b) in the slope formula

Slope =  [y₂ - y₁] /  [x₂ - x₁]

2 = [b - 2] / [4 - 2]

2(4 - 2) = b - 2

8 - 4 =b - 2

4 = b - 2

b = 6

Therefore, the value of b = 6

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