Question

1. knitting mel is knitting a scarf with diagonal stripes. before she began, she laid out the pattern on a coordinate grid where each unit represented 2 inches. on the grid, the first stripe began at (2, 0) and ended at (5, 4). all of the stripes are the same length. how many inches long is each stripe in the scarf? 15) art a terracotta bowl artifact has a triangular pattern around the top, as shown. all the triangles are about the same size and can be represented on a coordinate plane with vertices at points a(0, 6.8), b(4.5, 6.8), and c(2.25, 0). if each unit represents 1 centimeter, what is the approximate perimeter of each triangle, to the nearest tenth of a centimeter?

Explanation:

Question 14

Step1: Find the distance between the two points on the grid.

The distance formula between two points \((x_1, y_1)\) and \((x_2, y_2)\) is \(d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\). Here, \((x_1, y_1) = (2, 0)\) and \((x_2, y_2) = (5, 4)\). So, \(x_2 - x_1 = 5 - 2 = 3\) and \(y_2 - y_1 = 4 - 0 = 4\). Then \(d=\sqrt{3^2 + 4^2}=\sqrt{9 + 16}=\sqrt{25} = 5\) units.

Step2: Convert units to inches.

Each unit is 2 inches, so the length in inches is \(5\times2 = 10\) inches.

Step1: Find the length of \(AB\).

Points \(A(0, 6.8)\) and \(B(4.5, 6.8)\) have the same \(y\)-coordinate, so the distance \(AB\) is the absolute difference of the \(x\)-coordinates. \(AB=\vert4.5 - 0\vert = 4.5\) cm.

Step2: Find the length of \(AC\).

Using the distance formula \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\) for \(A(0, 6.8)\) and \(C(2.25, 0)\). \(x_2 - x_1 = 2.25 - 0 = 2.25\), \(y_2 - y_1 = 0 - 6.8=-6.8\). Then \(AC=\sqrt{(2.25)^2+(-6.8)^2}=\sqrt{5.0625 + 46.24}=\sqrt{51.3025}\approx7.16\) cm.

Step3: Find the length of \(BC\).

Since the triangle is isoceles (because \(A\) and \(B\) are horizontal, and \(C\) is on the vertical line of symmetry), \(BC = AC\approx7.16\) cm.

Step4: Calculate the perimeter.

Perimeter \(= AB + AC + BC = 4.5+7.16 + 7.16 = 18.82\approx18.8\) cm (to the nearest tenth).

Answer:

10

Question 15