Math Problem Statement

Determine the gradient of 𝐴𝐡.

Solution

To determine the gradient (or slope) of the line ABAB, you can use the formula for the slope between two points A(x1,y1)A(x_1, y_1) and B(x2,y2)B(x_2, y_2):

slope=m=y2βˆ’y1x2βˆ’x1\text{slope} = m = \frac{y_2 - y_1}{x_2 - x_1}

Given the points A(2,1)A(2, 1) and B(βˆ’4,βˆ’3)B(-4, -3):

  • x1=2x_1 = 2, y1=1y_1 = 1
  • x2=βˆ’4x_2 = -4, y2=βˆ’3y_2 = -3

Now, plug in the values:

m=βˆ’3βˆ’1βˆ’4βˆ’2=βˆ’4βˆ’6=23m = \frac{-3 - 1}{-4 - 2} = \frac{-4}{-6} = \frac{2}{3}

So, the gradient of ABAB is 23\frac{2}{3}.

Would you like further details or have any questions?

Here are 5 related questions:

  1. How do you find the length of a line segment between two points?
  2. What is the significance of the slope in a linear equation?
  3. How can you determine if two lines are parallel or perpendicular using their slopes?
  4. What is the equation of the line passing through points A(2,1)A(2, 1) and B(βˆ’4,βˆ’3)B(-4, -3)?
  5. How would you find the area of triangle ABCABC using the given coordinates?

Tip: Remember that the slope of a line indicates the direction and steepness of the line. A positive slope means the line ascends from left to right, while a negative slope means it descends.

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Math Problem Analysis

Mathematical Concepts

Analytical Geometry
Linear Equations

Formulas

Slope formula: m = (y2 - y1) / (x2 - x1)

Theorems

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Suitable Grade Level

Grades 7-9