# If point A(7,k) is the vertex of an isosceles triangle ABC with base BC, where B=(2,4) and C=(6,10), then what is k?

Then teach the underlying concepts
Don't copy without citing sources
preview
?

#### Explanation

Explain in detail...

#### Explanation:

I want someone to double check my answer

8
CW Share
May 14, 2017

$k = 5$

#### Explanation:

An isosceles triangle is a triangle with at least two equal sides. In an isosceles triangle that has exactly two equal sides, the equal sides are called legs and the third side is called the base. The vertex opposite the base is called the apex.

Given $B C$ is the base and $A \left(7 , k\right)$ is the apex, $\implies A B \mathmr{and} A C$ are the two equal sides.
$\implies A B = A C$
$\implies \sqrt{{\left(2 - 7\right)}^{2} + {\left(4 - k\right)}^{2}} = \sqrt{{\left(6 - 7\right)}^{2} + {\left(10 - k\right)}^{2}}$
$\implies {\left(2 - 7\right)}^{2} + {\left(4 - k\right)}^{2} = {\left(6 - 7\right)}^{2} + {\left(10 - k\right)}^{2}$
$\implies 25 + 16 - 8 k + \cancel{{k}^{2}} = 1 + 100 - 20 k + \cancel{{k}^{2}}$
$\implies 25 + 16 - 8 k = 1 + 100 - 20 k$
$\implies - 8 k + 20 k = 1 + 100 - 25 - 16$
$\implies 12 k = 60$
$\implies k = \frac{60}{12} = 5$

• 8 minutes ago
• 8 minutes ago
• 9 minutes ago
• 9 minutes ago
• A minute ago
• 3 minutes ago
• 3 minutes ago
• 5 minutes ago
• 8 minutes ago
• 8 minutes ago
• 8 minutes ago
• 8 minutes ago
• 9 minutes ago
• 9 minutes ago