Question

question 4 of 5 select the correct response from each dropdown menu. quadrilateral jklm has vertices of j(0,0), k(0,a), l(4a,4a), m(a,0). what are the steps to complete the proof to show jklm is a kite? quadrilateral jklm has vertices of j(0,0), k(0,a), l(4a,4a), m(a,0) is given. using the distance formula, the length of kj is a units, and the length of kl and ml is 5a units. and mj is a the slope of km is undefined and the slope of jl is 1 since adjacent side quadrilateral jklm is a kite.

Explanation:

Step1: Recall distance - formula

The distance formula between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\).

Step2: Find the length of \(\overline{KJ}\)

For points \(K(0,a)\) and \(J(0,0)\), \(x_1 = 0,y_1=a,x_2 = 0,y_2 = 0\). Substitute into the distance formula: \(d=\sqrt{(0 - 0)^2+(0 - a)^2}=\sqrt{0 + a^2}=a\).

Step3: Recall slope - formula

The slope formula between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(m=\frac{y_2 - y_1}{x_2 - x_1}\).

Step4: Find the slope of \(\overline{KM}\)

For points \(K(0,a)\) and \(M(a,0)\), \(x_1 = 0,y_1=a,x_2=a,y_2 = 0\). Then \(m=\frac{0 - a}{a - 0}=\frac{-a}{a}=- 1\).

Step5: Find the slope of \(\overline{JL}\)

For points \(J(0,0)\) and \(L(4a,4a)\), \(x_1 = 0,y_1 = 0,x_2=4a,y_2 = 4a\). Then \(m=\frac{4a-0}{4a - 0}=1\).

Answer:

The length of \(\overline{KJ}\) is \(a\) units, the slope of \(\overline{KM}\) is \(-1\), and the slope of \(\overline{JL}\) is \(1\).