Question

If the 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'?

Answer 1

See the attach file for ur ans

Answer 2

Answer:

The value of k is 5.

Step-by-step explanation:

Given A(7,K), B(2.4) and C(6,10)

ABC form an isosceles triangle

Hence AB = AC

$\begin{array}{l}{(\mathrm{AB})^{2}=(\mathrm{AC})^{2}} \\ {(7-2)^{2}+(\mathrm{K}-4)^{2}=(7-6)^{2}+(\mathrm{K}-10)^{2}} \\ {(5)^{2}+(\mathrm{K}-4)^{2}=(1)^{2}+(\mathrm{K}-10)^{2}} \\ {25+\mathrm{K}^{2}+16-8 \mathrm{K}=1+\mathrm{K}^{2}+100-20 \mathrm{K}} \\ {41+\mathrm{K}^{2}-8 \mathrm{K}=101+\mathrm{K}^{2}-20 \mathrm{K}}\end{array}$

41 – 8K = 101 – 20K

20K – 8K = 101 – 41

12 K = 60

K = 5