Question

name the type of quadrilateral formed by the following points and give reasons for your answer : (-1,-2) , (1,0) , (-1,2) , (-3,0)

Answer 1

$\huge{\pink{\underline{\ulcorner{\star\: Solution\: \star}\urcorner}}}$


$A(-1,-2) \\ B(1,0) \\ C(-1,2)\\ D(-3,0)$

$x_1 = -1 , y_1 = -2 \\ x_2=1 , y_2 = 0 \\ x_3= -1 , y_3= 2 \\ x_4 = -3 , y_4= 0$

AB , BC , CD , DA

$AB \: = \sqrt{(x_2-x_1)^{2} + (y_2-y_1)^{2}}\\\implies \sqrt{(1-(-1))^{2} + (0-(-2))^{2}}\\\implies \sqrt{(1+1))^{2} + (0+2)^{2}}\\\implies \sqrt{4+4} \\\implies 2\sqrt{2}\: unit$

$BC\: = \sqrt{(x_3-x_2)^{2} + (y_3-y_2)^{2}}\\\implies \sqrt{(-1-1)^{2} + (2-0)^{2}}\\\implies \sqrt{(-2)^{2} + (2)^{2}}\\\implies \sqrt{4+4} \\\implies 2\sqrt{2}\:unit$

$CD \: = \sqrt{(x_4-x_3)^{2} + (y_4-y_3)^{2}}\\\implies \sqrt{(-3+1)^{2} + (0-2)^{2}}\\\implies \sqrt{(-2)^{2} + (-2)^{2}}\\\implies \sqrt{4+4} \\\implies 2\sqrt{2}\:unit$

$DA \: = \sqrt{(x_1-x_4)^{2} + (y_1-y_4)^{2}}\\\implies \sqrt{(-1+3)^{2} + (-2-0)^{2}}\\\implies \sqrt{(2))^{2} + (-2)^{2}}\\\implies \sqrt{4+4} \\\implies 2\sqrt{2}\:unit$

2√2 unit =AB=BC=CD=DA

---(eqt 1)

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Now checking diagonal's

$AC\: = \sqrt{(x_3-x_1)^{2} + (y_3-y_1)^{2}}\\\implies \sqrt{(-1+1)^{2} + (2+2)^{2}}\\\implies \sqrt{(0))^{2} + (4)^{2}}\\\implies \sqrt{16} \\\implies 4\: unit$

$BD \: = \sqrt{(x_4-x_2)^{2} + (y_4-y_2)^{2}}\\\implies \sqrt{(-3-1)^{2} + (0-0)^{2}}\\\implies \sqrt{(-4)^{2} + (0)^{2}}\\\implies \sqrt{16} \\\implies 4\: unit$

AC = BD

----(eqt 2)

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All sides are equal.

AB = BC = CD = DA (2√2 unit)

Diagonal's are equal.

AC = BD (4 unit)


$\red{\underline{Answer}}$
Type : The given quadrilateral is SQUARE.



Thanks

Answer 2

Answer:

Step-by-step explanation:

Name the type of quadrilateral formed, if any, by the following points and give reasons for your answer.

(-1, -2), (1,0), (-1, 2), (-3, 0)

(4, 5), (7, 6), (4, 3), (1, 2)