Question

Help with geometry!!!!!

Answer 1

• AB = AC = 5 units
• BC = 6 units
• No it is not a equilateral triangle

Explanation:

Some coordinates of a triangle is given to us. And we need to find the length of AB , BC and AC . The given coordinates are ,

`\rm\implies Coordinates = A(-1,3) , B(2,-1) \ and \ C(-4,-1)`

We can use the Distance Formula to find the length of sides of the triangle .

Finding length of AB :-

`\rm\implies Distance =√( ( x_2-x_1)^2+(y_2-y_1)^2) \\\\\rm\implies \overline{AB}= √( (-1-2)^2+(-1-3)^2) \\\\\rm\implies \overline{AB}= √( (-3)^2+(-4)^2) \\\\\rm\implies \overline{AB}= √( 9 + 16) \\\\\rm\implies \overline{AB}= √(25) \\\\\rm\implies\boxed{\red{\rm \overline{AB}= 5 \ units}}`

Finding length of AC :-

`\rm\implies Distance =√( ( x_2-x_1)^2+(y_2-y_1)^2) \\\\\rm\implies \overline{AC}= √( (-1+4)^2+(-1-3)^2 )\\\\\rm\implies \overline{AC}= √( (-3)^2+(-4)^2) \\\\\rm\implies \overline{AC}= √( 9 + 16) \\\\\rm\implies \overline{AC}= √(25) \\\\\rm\implies\boxed{\red{\rm \overline{AC}= 5 \ units}}`

Finding length of BC :-

`\rm\implies Distance =√( ( x_2-x_1)^2+(y_2-y_1)^2) \\\\\rm\implies \overline{BC}= √( (-4-2)^2+(-1-1)^2) \\\\\rm\implies \overline{BC}= √( 6^2+0^2) \\\\\rm\implies \overline{BC}= √( 36+0) \\\\\rm\implies \overline{BC}= √(36) \\\\\rm\implies\boxed{\red{\rm \overline{BC}= 6 \ units}}`

Is it a Equilateral triangle ?

No the given triangle is not a equilateral triangle since the measure of all sides is not same.

Answer 2

NO

Explanation:

To find the length of AB

AB = sqrt( (x2-x1)^2 + (y2-y1)^2)

= sqrt ( ( 2 - -1)^2+ ( -1 -3)^2)

= sqrt( 3^2 + (-4)^2)

= sqrt(9+16)

= sqrt(25)

= 5

To find the length of AC

AC = sqrt( (x2-x1)^2 + (y2-y1)^2)

= sqrt ( ( -4 - -1)^2+ ( -1 -3)^2)

= sqrt( ( -3)^2 + (-4)^2)

= sqrt(9+16)

= sqrt(25)

= 5

To find the length of BC

BC = sqrt( (x2-x1)^2 + (y2-y1)^2)

= sqrt ( ( -4-2)^2+ ( -1 --1)^2)

= sqrt( ( -6)^2 + (0)^2)

= sqrt(36)

= 6

This is not an equilateral triangle since BC is not equal to AB = AC