a grid map marks the plot of harolds garden in meters. the coordinates of the quadrilateral-shaped property are $g(-8, 3)$, $a(4, 8)$, $r(10, 0)$, and $d(-2, -5)$. he wants to build a short fence around the garden.

the perimeter of his garden is meters.

Question

a grid map marks the plot of harolds garden in meters. the coordinates of the quadrilateral-shaped property are \$g(-8, 3)\$, \$a(4, 8)\$, \$r(10, 0)\$, and \$d(-2, -5)\$. he wants to build a short fence around the garden.

the perimeter of his garden is meters.

the perimeter of his garden is   meters.

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Distance Formula", "Perimeter in Coordinate Plane" ], "new_concepts": [], "current_concepts": [ "Distance Formula", "Perimeter in Coordinate Plane" ] } ## Identify the vertices of the quadrilateral Using the *Perimeter in Coordinate Plane* knowledge point The coordinates of the vertices of the garden are given as: - $G(-8, 3)$ - $A(4, 8)$ - $R(10, 0)$ - $D(-2, -5)$ ## Calculate the length of side GA Using the *Distance Formula* knowledge point $$ \begin{aligned} GA &= \sqrt{(4 - (-8))^2 + (8 - 3)^2} \ &= \sqrt{(12)^2 + (5)^2} \ &= \sqrt{144 + 25} \ &= \sqrt{169} \ &= 13 \end{aligned} $$ ## Calculate the length of side AR Using the *Distance Formula* knowledge point $$ \begin{aligned} AR &= \sqrt{(10 - 4)^2 + (0 - 8)^2} \ &= \sqrt{(6)^2 + (-8)^2} \ &= \sqrt{36 + 64} \ &= \sqrt{100} \ &= 10 \end{aligned} $$ ## Calculate the length of side RD Using the *Distance Formula* knowledge point $$ \begin{aligned} RD &= \sqrt{(-2 - 10)^2 + (-5 - 0)^2} \ &= \sqrt{(-12)^2 + (-5)^2} \ &= \sqrt{144 + 25} \ &= \sqrt{169} \ &= 13 \end{aligned} $$ ## Calculate the length of side DG and total perimeter Using the *Distance Formula* and *Perimeter in Coordinate Plane* knowledge points $$ \begin{aligned} DG &= \sqrt{(-8 - (-2))^2 + (3 - (-5))^2} \ &= \sqrt{(-6)^2 + (8)^2} \ &= \sqrt{36 + 64} \ &= \sqrt{100} \ &= 10 \end{aligned} $$ $$ \begin{aligned} \text{Perimeter} &= GA + AR + RD + DG \ &= 13 + 10 + 13 + 10 \ &= 46 \end{aligned} $$ A grid map marks the plot of Harold's garden in meters. The coordinates of the quadrilateral-shaped property are G(-8, 3), A(4, 8), R(10, 0), and D(-2, -5). He wants to build a short fence around the garden. The perimeter of his garden is 46 meters. { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Geometry", "Perimeter in Coordinate Plane" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the vertices of the quadrilateral

Calculate the length of side GA

Calculate the length of side AR

Calculate the length of side RD

Calculate the length of side DG and total perimeter

Answer: