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Finding the slopes of JM and KL

[tex] Slope\;\;JM\;=\; \frac{2-1}{3-2} \;=\;1\\\\
Slope\;\;KL\;=\;\frac{2-(-3)}{7-2}\;=\;\frac{5}{5} \;=\;1 [/tex]

⇒ Slope of JM = Slope of KL = 1, it means JM║KL

Finding distances JK and ML

JK = 4 units and ML = 4 units, so JK = ML

Since we have JM║KL and JK = ML, we can say JKLM is an isosceles trapezoid.

Answer:

B. Isosceles trapezoid.

Step-by-step explanation:

We have been given an image of quadrilateral JKLM on coordinate plane. We are asked to determine the most precise name for quadrilateral.

We can see that our given quadrilateral looks like a trapezoid. We know that a trapezoid has a pair of parallel sides.

Let us find slope of segment JM and KL using given coordinates.

[tex]\text{Slope of segment JM}=\frac{2-1}{3-2}[/tex]

[tex]\text{Slope of segment JM}=\frac{1}{1}[/tex]

[tex]\text{Slope of segment JM}=1[/tex]

[tex]\text{Slope of segment KL}=\frac{2--3}{7-2}[/tex]

[tex]\text{Slope of segment KL}=\frac{2+3}{5}[/tex]

[tex]\text{Slope of segment KL}=\frac{5}{5}[/tex]

[tex]\text{Slope of segment KL}=1[/tex]

Since slope of Segment JM is equal to slope of segment Kl, therefore, [tex]JM||KL[/tex]

We can also see that both legs of trapezoid (Ml and JK) are 4 units long, so base angles of our given trapezoid will be equal.

We know that both legs of an isosceles trapezoid are equal, therefore, our given quadrilateral is an isosceles trapezoid and option B is the correct choice.

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