Question

triangle xyz, with vertices x(-7,-7), y(-4,-5), and z(-6,-4), is drawn on the coordinate grid below.

Explanation:

Since the problem statement is incomplete (no specific question about the triangle is provided, like finding side length, area, type, or a transformation), we can't proceed with a solution. If you want to find something like the length of a side, area, or check the type of triangle, please provide that specific question. For example, if you want to find the length of XY, we can use the distance formula. Let's assume the question is "Find the length of side XY of triangle XYZ with vertices X(-7,-7), Y(-4,-5), and Z(-6,-4)." Then we can solve it as follows:

Step1: Recall the distance formula

The distance between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by \(d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\).

Step2: Identify the coordinates

For points X(-7, -7) and Y(-4, -5), we have \(x_1 = -7\), \(y_1 = -7\), \(x_2 = -4\), \(y_2 = -5\).

Step3: Substitute into the formula

\[

$$\begin{align*} d_{XY}&=\sqrt{(-4 - (-7))^2 + (-5 - (-7))^2}\\ &=\sqrt{(-4 + 7)^2 + (-5 + 7)^2}\\ &=\sqrt{(3)^2 + (2)^2}\\ &=\sqrt{9 + 4}\\ &=\sqrt{13} \end{align*}$$

\]

Answer:

The length of side XY is \(\sqrt{13}\) units.