Find length of AB. 2. Calculate the coordinates of midpoint of line AC. 3. Calculate the gradient of AC.

Question

ScanSolve AI Tutor · Accepted Answer

Okay Pop's, let's tackle the next parts of this problem.

2) Calculate the coordinates of the midpoint of line AC.

To find the midpoint of a line segment with endpoints $(x_1, y_1)$ and $(x_2, y_2)$ , we use the midpoint formula:

M = \left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right)

Identify the coordinates of points A and C.
Point A is $(2, 3)$ , so $x_1 = 2$ and $y_1 = 3$ .
Point C is $(4, 6)$ , so $x_2 = 4$ and $y_2 = 6$ .
Substitute the coordinates into the midpoint formula.
$M = \left(\frac{2 + 4}{2}, \frac{3 + 6}{2}\right)$
Simplify the expression.
$M = \left(\frac{6}{2}, \frac{9}{2}\right)$ $M = \left(3, 4.5\right)$
The coordinates of the midpoint of AC are $\boxed{(3, 4.5)}$ .

3) Calculate the gradient of AC.

To find the gradient (slope) of a line segment with endpoints $(x_1, y_1)$ and $(x_2, y_2)$ , we use the gradient formula:
$m = \frac{y_2 - y_1}{x_2 - x_1}$
Identify the coordinates of points A and C.
Point A is $(2, 3)$ , so $x_1 = 2$ and $y_1 = 3$ .
Point C is $(4, 6)$ , so $x_2 = 4$ and $y_2 = 6$ .
Substitute the coordinates into the gradient formula.
$m = \frac{6 - 3}{4 - 2}$
Simplify the expression.
$m = \frac{3}{2}$ $m = 1.5$
The gradient of AC is $\boxed{1.5}$ .

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