Question

If points A(4,5), B(1,1) and C (-2,5) are vertices of an isosceles triangle, determine length of each leg;

Answer 1

Remember that

The formula to calculate the distance between two points is equal to

`d=\sqrt[]{(y2-y1)^2+(x2-x1)^2}`

step 1

Find the length of leg AB

A(4,5), B(1,1)

substitute the given coordinates in the formula

`AB=\sqrt[]{(1-5)^2+(1-4)^2}`
`\begin{gathered} AB=\sqrt[]{(-4)^2+(-3)^2} \\ AB=\sqrt[]{25} \\ AB=5 \end{gathered}`

step 2

Find out the length of leg BC

B(1,1) and C (-2,5)

substitute the given coordinates in the formula

`BC=\sqrt[]{(5-1)^2+(-2-1)^2}`
`\begin{gathered} BC=\sqrt[]{(4)^2+(-3)^2} \\ BC=5 \end{gathered}`

step 3

Find out the length of leg AC

A(4,5), and C (-2,5)

substitute the given coordinates in the formula

`AC=\sqrt[]{(5-5)^2+(-2-4)^2}`
`\begin{gathered} AC=\sqrt[]{(0)^2+(-6)^2} \\ AC=6 \end{gathered}`