Question

13 given parallelogram abcd as shown, find the length of diagonal from a to c. image of coordinate grid with points a, b, c, d a $sqrt{61}$ b $sqrt{11}$ c $sqrt{117}$ d 15

Explanation:

Step1: Identify coordinates of A and C

From the grid, point A is at (2, 3) and point C is at (7, 9).

Step2: Apply distance formula

The distance formula between two points \((x_1, y_1)\) and \((x_2, y_2)\) is \(d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\).
Substitute \(x_1 = 2\), \(y_1 = 3\), \(x_2 = 7\), \(y_2 = 9\):
\(d = \sqrt{(7 - 2)^2 + (9 - 3)^2}\)
\(d = \sqrt{5^2 + 6^2}\)
\(d = \sqrt{25 + 36}\)
\(d = \sqrt{61}\)

Answer:

A. \(\sqrt{61}\)