Expressing Geometric Properties with Equations (G.GPE)

Jayesh is buying supplies for his garden, modeled in the graph below. Each unit represents 1 foot. How many feet of fence does Jayesh need to surround his garden?

• 10 feet

• 18 feet

• 26 feet

• 36 feet

A square has a side with endpoints (6, –4) and (–2, 2). What is the area of the square, do not include units?

A square has a side with endpoints (6, –4) and (–2, 2). What is the perimeter of the square, do not include units?

The area of an isosceles triangle is 28 square units, and its base has endpoints (4, –4) and (–3, –4). What is the third vertex of the triangle, if the third vertex is above the base? Write your answer as an ordered pair.

Consider points A(–2, 3), B(4, –5), and C(a, b). Find a and b so that ΔABC is an isosceles triangle with base AB and the sum of the coordinates of C is 7. What are the coordinates of point C? Write your answer as an ordered pair.

What is the distance between the two points on the graph?

• √29

• 29

• √65

• 65

Maria makes a diagram of a wall where each unit represents 1 foot. It will cost her $4 per square foot to paint the wall. What will the total painting cost be?

• $240

• $640

• $960

• $1280

Select all points that are the same distance from (4, 6) as (7, 4).

• (7, 8)

• (1, 4)

• (7, 0)

• (0, 4)

• (1, 8)

Select all the values that can be a side length of the triangle.

• √97

• √65

• 5√2

• √53

• √34

A circle has center at C(0, 0). Point P(3, √15) lies on the circle. What is the radius of the circle?

• 2

• 3

• 24

• √24