Question

On a coordinate plane, triangle A B C is shown. Point A is at (negative 1, 6), point B is at (negative 1, 1), and point C is at (2, 2). Triangle ABC is an isosceles triangle in which AB = AC. What is the perimeter of △ABC? 5 + StartRoot 10 EndRoot units StartRoot 10 EndRoot units 10 + StartRoot 10 EndRoot units 15 units

Answer 1

10 +√10

Explanation:

Given the coordinates of the triangle expressed asA(-1,6), B(-1, 1) and C(2,2)

The perimeter of the triangle= AB + BC + AC

Since AB = ACP = AC + BC + ACP = 2AC + BC

get the length AC using the formula;

Given A(-1,6) and C(2,2)AC = √(2-(-1))²+(2-6)AC = √3²+4²AC = √9+16AC = √25AC = 5

Get BCB(-1, 1) and C(2,2)BC = √(2-(-1))²+(2-1)BC = √3²+1²BC = √9+1BC = √10 Perimeter = 2(5)+√10 Perimeter = 10 + √10

Hence the perimeter of the triangle is 10 +√10

Answer 2

10 +√10

Explanation:

Given the coordinates of the triangle expressed as

A(-1,6), B(-1, 1) and C(2,2)

The perimeter of the triangle= AB + BC + AC\

Since AB = AC

P = AC + BC + AC

P = 2AC + BC

get the length AC using the formula;

Given A(-1,6) and C(2,2)

AC = √(2-(-1))²+(2-6)

AC = √3²+4²

AC = √9+16

AC = √25

AC = 5

Get BC

B(-1, 1) and C(2,2)

BC = √(2-(-1))²+(2-1)

BC = √3²+1²

BC = √9+1

BC = √10

Perimeter = 2(5)+√10

Perimeter = 10 + √10

Hence the perimeter of the triangle is 10 +√10