Question

Figure LMNO is located at L (1, 1), M (4, 4), N (7, 1), and O (4,-2). Use coordinate geometry to best classify quadrilateral LMNO. A. Kite B. Parallelogram C. Square D. Trapezoid

Answer 1

Answer:

Square (B)

Step-by-step explanation:

I just took the test and I got this question right. if you want and explaination though you can just look above.

Answer 2

Coordinates given in the question define the structure as square. Option A is the answer.

 Geometrical shapes,

• Square - All sides of the quadrilateral equal and all inner angles measure 90°.

• Kite - 1). Two pairs of consecutive congruent sides.

                 2). Congruent non vertex angles.

                 3). Perpendicular diagonals.

• Parallelogram - Opposite sides are congruent and parallel.
• Trapezoid - One pair of parallel sides.

Given in the question,

• Coordinates of the vertices → L(1, 1), M(4, 4), N(7, 1) and O(4, -2)

Graph the points to analyze the shape.

Use the formula for the distance between two points (x₁, y₁) and (x₂, y₂)

Distance = $\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

LM = $\sqrt{(4-1)^2+(4-1)^2}$

     = $\sqrt{18}$

MN = $\sqrt{(7-4)^2+(1-4)^2}$

      = $\sqrt{18}$

NO = $\sqrt{(7-4)^2+(1+2)^2}$

      = $\sqrt{18}$

OL  = $\sqrt{(1-4)^2+(1+2)^2}$

      = $\sqrt{18}$

This explains LM = MN = NO = OL.

    Therefore, by the property of a square, LMNO will be a SQUARE.

Learn more about the geometrical shapes here,

https://brainly.com/question/2135964?referrer=searchResults