The xy-plane shows triangle ABC. The coordinates of A, B and C are (−4,6), (8,−2) and (2,−2) respectively. (a) Calculate coordinates of the midpoint of line AB.

a) Step 1: Recall the midpoint formula for two points (x₁, y₁) and (x₂, y₂): M = ((x₁+x₂)/(2), (y₁+y₂)/(2)) Step 2: Identify the coordinates of points A and B. A = (−4, 6) so x₁ = −4, y₁ = 6. B = (8, −2) so x₂ = 8, y₂ = −2. Step 3: Substitute the coordinates into the midpoint formula and calculate. M = ((−4+8)/(2), (6+(−2))/(2)); M = (4/2, 4/2); M = (2, 2) The coordinates of the midpoint of line AB are (2, 2).

The xy-plane shows triangle ABC. The coordinates of A, B and C are (−4,6), (8,−2) and (2,−2) respectively. (a) Calculate coordinates of the midpoint of line AB.

a) Step 1: Recall the midpoint formula for two points (x₁, y₁) and (x₂, y₂): M = ((x₁+x₂)/(2), (y₁+y₂)/(2)) Step 2: Identify the coordinates of points A and B. A = (−4, 6) so x₁ = −4, y₁ = 6. B = (8, −2) so x₂ = 8, y₂ = −2. Step 3: Substitute the coordinates into the midpoint formula and calculate. M = ((−4+8)/(2), (6+(−2))/(2)); M = (4/2, 4/2); M = (2, 2) The coordinates of the midpoint of line AB are (2, 2).

Solved: The xy-plane shows triangle ABC. The coordinates of…

Recall the midpoint formula for two points $(x_1, y_1)$ and $(x_2, y_2)$
$M = \left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)$
Identify the coordinates of points A and B.
$A = (-4, 6)$ so $x_1 = -4$ , $y_1 = 6$ .
$B = (8, -2)$ so $x_2 = 8$ , $y_2 = -2$ .
Substitute the coordinates into the midpoint formula and calculate.
$M = \left(\frac{-4+8}{2}, \frac{6+(-2)}{2}\right)$ $M = \left(\frac{4}{2}, \frac{4}{2}\right)$ $M = (2, 2)$
The coordinates of the midpoint of line AB are $(2, 2)$ .

The xy-plane shows triangle ABC. The coordinates of A, B and C are (-4,6), (8,-2) and (2,-2) respectively. (a) Calculate coordinates of the midpoint of line AB.

Answer

Step-by-step solution

Recall the midpoint formula for two points $(x_1, y_1)$ and $(x_2, y_2)$

Identify the coordinates of points A and B.

Substitute the coordinates into the midpoint formula and calculate.

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