CUET PG 2023 — Mathematics PYQ

Step 1: Sides ki length nikaalna

• Side $AB$ ki length:

  $$AB=\sqrt{(-1-4{)}^2+(-1-0{)}^2}$$
  $$AB=\sqrt{(-5{)}^2+(-1{)}^2}=\sqrt{25+1}=\sqrt{26}$$

• Side $BC$ ki length:

  $$BC=\sqrt{(3-(-1){)}^2+(5-(-1){)}^2}$$
  $$BC=\sqrt{(4{)}^2+(6{)}^2}=\sqrt{16+36}=\sqrt{52}$$

• Side $CA$ ki length:

  $$CA=\sqrt{(4-3{)}^2+(0-5{)}^2}$$
  $$CA=\sqrt{(1{)}^2+(-5{)}^2}=\sqrt{1+25}=\sqrt{26}$$

Step 2: Properties check karna

Humein do important cheezein dikh rahi hain:

1. Isosceles property: Do sides barabar hain ($AB=CA=\sqrt{26}$).

2. Right-angled property: Pythagoras theorem check karte hain ($A{B}^2+C{A}^2=B{C}^2$):

   $$(\sqrt{26}{)}^2+(\sqrt{26}{)}^2=26+26=52$$

   Kyunki $(\sqrt{52}{)}^2=52$, isliye $A{B}^2+C{A}^2=B{C}^2$ satisfy ho raha hai.

   Answer: It is an Isosceles Right-angled Triangle.