Find the gradient, equation, and midpoint of the line segment joining points A (−2, 6) and B (10, 8).

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Given points: Point A (−2, 6) and Point B (10, 8). a) To find the gradient of the line passing through A and B. Step 1: Use the gradient formula m = (y₂ − y₁)/(x₂ − x₁). Let (x₁, y₁) = (−2, 6) and (x₂, y₂) = (10, 8). m = (8 − 6)/(10 − (−2)) Step 2: Calculate the gradient. m = (2)/(10 + 2); m = 2/12; m = 1/6; b) To find the equation of the beam passing through A and B in the form y = mx + c. Step 1: Use the gradient m = 1/6 from part (a) and point A (−2, 6) in the point-slope form y − y₁ = m(x − x₁). y − 6 = 1/6(x − (−2)); y − 6 = 1/6(x + 2); Step 2: Rearrange the equation into y = mx + c form. y − 6 = 1/6x + 2/6; y − 6 = 1/6x + 1/3 Add 6 to both sides: y = 1/6x + 1/3 + 6; y = 1/6x + 1/3 + 18/3; y = 1/6x + 19/3 c) To find the midpoint of the straight line joining A and B. Step 1: Use the midpoint formula M = ((x₁ + x₂)/(2), (y₁ + y₂)/(2)). Let (x₁, y₁) = (−2, 6) and (x₂, y₂) = (10, 8). M = ((−2 + 10)/(2), (6 + 8)/(2)) Step 2: Calculate the coordinates of the midpoint. M = (8/2, 14/2); M = (4, 7)

Find the gradient, equation, and midpoint of the line segment joining points A (-2, 6) and B (10, 8).

Answers

Step-by-step solution

Part a· 2 steps

Use the gradient formula $m = \frac{y_2 - y_1}{x_2 - x_1}$ .

Calculate the gradient.

Part b· 2 steps
$\frac{1}{6}x + \frac{19}{3}$

Use the gradient $m = \frac{1}{6}$ from part (a) and point A $(-2, 6)$ in the point-slope form $y - y_1 = m(x - x_1)$ .

Rearrange the equation into $y = mx + c$ form.

Part c· 2 steps(4, 7)

Use the midpoint formula $M = \left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right)$ .

Calculate the coordinates of the midpoint.

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