Answer
JK = √(68)
KL = √(68)
JL = √(72)
From this, we can see that two of the three sides of the triangle are of the same lengths, hence, we can confirm that this triangle is an isoscelles triangle.
Step-by-step explanation
The distance between two points with the coordinates (x₁, y₁) and (x₂, y₂) is given as
d = √[(x₂ - x₁)² + (y₂ - y₁)²]
Starting with J(-7, -7) and K(-9, 1)
x₁ = -7
y₁ = -7
x₂ = -9
y₂ = 1
d = √[(x₂ - x₁)² + (y₂ - y₁)²]
JK = √[(-9 - (-7))² + (1 - (-7))²]
JK = √[(-9 + 7)² + (1 + 7)²]
JK = √[(-2)² + (8)²]
JK = √[4 + 64]
JK = √(68)
K(-9, 1) and L(-1, -1)
x₁ = -9
y₁ = 1
x₂ = -1
y₂ = -1
d = √[(x₂ - x₁)² + (y₂ - y₁)²]
KL = √[(-1 - (-9))² + (-1 - 1)²]
KL = √[(-1 + 9)² + (-2)²]
KL = √[(8)² + (-2)²]
KL = √(64 + 4)
KL = √(68)
J(-7, -7) and L(-1, -1)
x₁ = -7
y₁ = -7
x₂ = -1
y₂ = -1
d = √[(x₂ - x₁)² + (y₂ - y₁)²]
JL = √[(-1 - (-7))² + (-1 - (-7))²]
JL = √[(-1 + 7)² + (-1 + 7)²]
JL = √[6² + 6²]
JL = √(36 + 36)
JL = √(72)
JK = √(68)
KL = √(68)
JL = √(72)
From this, we can see that two of the three sides of the triangle are of the same lengths, hence, we can confirm that this triangle is an isoscelles triangle.
Hope this Helps!!!