Week 1

Julie is given two points, (x, y) and (w, z). Which process can she use to find the distance between the points?

• Count off the horizontal distance between x and w, and add the vertical distance between y and z.

• Count off the horizontal distance between x and y, and add the vertical distance between w and z.

• Subtract x – w and y – z. Square the differences, and then add the squares. Finally, take the square root of the sum.

• Subtract x – y and w – z. Square the differences, and then add the squares. Finally, take the square root of the sum.

A map of a small town identifies the town square as the origin (0, 0). Each block along a street is represented by one unit along the x- or y-axis. The ice cream shop is at (5, 4) and the grocery store is at (3, –2). The grocer wants to install an overhead delivery cable directly between the grocery store and the ice cream shop to expedite deliveries. What is the length of this cable to the nearest tenth of a block?

• 2.8 blocks

• 5.1 blocks

• 6.3 blocks

• 8.0 blocks

The distance between two points on a coordinate grid is 5 units. One of the points is at (2, –1). The x-coordinate of the other point is –2. Which is a possible value for the missing y-coordinate? Check all that apply.

• -4

• -2

• 0

• 1

• 2

The width of a rectangular rug is 7 feet, and the length of its diagonal is 25 feet. What is the area of the rug to the nearest square foot?

• $24\ ft^2$

• $26\ ft^2$

• $168\ ft^2$

• $182\ ft^2$

Oscar's dog house is shaped like a tent. The slanted sides are both 15 feet long and the bottom of the house is 18 feet across. What is the height of his dog house, in feet, at its tallest point?

• $12\ ft$

• $9\ ft$

• $15\ ft$

• $10\ ft$

If the square of the hypotenuse of an isosceles right triangle is 128 cm², find the length of each side.

• $8\sqrt{2}cm$

• $4\sqrt{2}cm$

• $64\ cm$

• $8\ cm$

Find the perimeter of a rectangle whose length is 150 m and the diagonal is 170 m.

• 80 m

• 460 m

• 380 m

• 230 m

The height of two building is 34 m and 29 m respectively. If the distance between the two building is 12 m, find the distance between their tops.

• 5 m

• 10 m

• 17 m

• 13 m

Which is the equation of a circle that contains the points Q(1,−2), R(9,−2), and S(9,2)?

• $\left(x-5\right)^2+y^2=40$
  

• $\left(x-5\right)^2+y^2=20$

• $x^2+\left(y-5\right)^2=89$

• $x^2+\left(y-5\right)^2=\sqrt{20}$

Which is the equation of a circle with its center at (−4,2) and a radius of 4?

• $\left(x-4\right)^2+\left(x+2\right)^2=4$

• $\left(x+4\right)^2+\left(x-2\right)^2=4$

• $\left(x-4\right)^2+\left(x+2\right)^2=16$

• $\left(x+4\right)^2+\left(x-2\right)^2=16$