Question

the graph shows triangles jkl and opq. is jkl similar to opq? justify your answer.

Explanation:

Step1: Find the lengths of the sides

Use the distance formula \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\) or count the units for vertical/horizontal sides.
For \(JK\): From \(J(-3,1)\) to \(K(2,-3)\), using the distance formula \(d=\sqrt{(2 + 3)^2+(-3 - 1)^2}=\sqrt{25 + 16}=\sqrt{41}\). For \(KL\): From \(K(2,-3)\) to \(L(-3,-2)\), \(d=\sqrt{(-3 - 2)^2+(-2+ 3)^2}=\sqrt{25 + 1}=\sqrt{26}\). For \(LJ\): From \(L(-3,-2)\) to \(J(-3,1)\), \(d=\sqrt{(-3+3)^2+(1 + 2)^2}=3\).
For \(OP\): From \(O(-3,1)\) to \(P(7,-7)\), \(d=\sqrt{(7 + 3)^2+(-7 - 1)^2}=\sqrt{100+64}=\sqrt{164}=2\sqrt{41}\). For \(PQ\): From \(P(7,-7)\) to \(Q(-3,-6)\), \(d=\sqrt{(-3 - 7)^2+(-6 + 7)^2}=\sqrt{100 + 1}=\sqrt{101}\). For \(QO\): From \(Q(-3,-6)\) to \(O(-3,1)\), \(d=\sqrt{(-3+3)^2+(1 + 6)^2}=7\).

Step2: Check the ratio of sides

\(\frac{JK}{OP}=\frac{\sqrt{41}}{2\sqrt{41}}=\frac{1}{2}\), \(\frac{LJ}{QO}=\frac{3}{7}
eq\frac{1}{2}\).

Answer:

No. The ratios of the corresponding sides are not equal.