Question

the vertices of a pair of figures are ( a(-8,-2) ), ( b(-4,2) ), ( c(-4,-2) ) and ( g(2,-1) ), ( h(4,-1) ), ( j(2,-3) ). determine whether a scale drawing is represented by the pair of figures. yes no

Explanation:

Step1: Calculate the length of \(BC\)

For \(B(-4,2)\) and \(C(-4, - 2)\), using the distance formula \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\). Here \(x_1=-4,y_1 = 2,x_2=-4,y_2=-2\).
\(BC=\sqrt{(-4+4)^2+(-2 - 2)^2}=\sqrt{0+(-4)^2}=4\)

Step2: Calculate the length of \(HJ\)

For \(H(4,-1)\) and \(J(2,-3)\), \(x_1 = 4,y_1=-1,x_2=2,y_2=-3\)
\(HJ=\sqrt{(2 - 4)^2+(-3 + 1)^2}=\sqrt{(-2)^2+(-2)^2}=\sqrt{4 + 4}=\sqrt{8}=2\sqrt{2}\)

Step3: Calculate the length of \(AC\)

For \(A(-8,-2)\) and \(C(-4,-2)\), \(x_1=-8,y_1=-2,x_2=-4,y_2=-2\)
\(AC=\sqrt{(-4 + 8)^2+(-2+2)^2}=\sqrt{4^2+0}=4\)

Step4: Calculate the length of \(GJ\)

For \(G(2,-1)\) and \(J(2,-3)\), \(x_1=2,y_1=-1,x_2=2,y_2=-3\)
\(GJ=\sqrt{(2 - 2)^2+(-3 + 1)^2}=\sqrt{0+(-2)^2}=2\)

Step5: Check the ratio of corresponding sides

\(\frac{BC}{HJ}=\frac{4}{2\sqrt{2}}=\sqrt{2}\), \(\frac{AC}{GJ}=\frac{4}{2}=2\)
Since \(\frac{BC}{HJ}
eq\frac{AC}{GJ}\), the figures are not similar (scale - drawing requires similarity, i.e., all corresponding sides are in proportion)

Answer:

no