Question

9. Find the point on the X-axis
10. If the distance between two points (x, 7) and (1, 15) is 10, find the value ofx.​

Answer 1

Distance between two points

Given: the distance between two points $(x,7)$ and $(1,15)$ is $10$ units

To find: the value of $x$

Solution:

• Rule: the distance between the two points $(x_{1},y_{1})$ and $(x_{2},y_{2})$ is
• $=\sqrt{(x_{1}-x_{2})^{2}+(y_{1}-y_{2})^{2}}$ units

Given that, the distance between the two points $(x,7)$ and $(1,15)$ is $10$ units

• $\Rightarrow \sqrt{(x-1)^{2}+(7-15)^{2}}=10$

• $\Rightarrow \sqrt{x^{2}-2x+1+64}=10$

• $\Rightarrow \sqrt{x^{2}-2x+65}=10$

• $\Rightarrow x^{2}-2x+65=100$

• $\Rightarrow x^{2}-2x-35=0$

• $\Rightarrow x^{2}-7x+5x-35=0$

• $\Rightarrow x(x-7)+5(x-5)=0$

• $\Rightarrow (x-7)(x+5)=0$

• $\Rightarrow x=7,\: -5$

Answer: the values of $x$ are $7,\: -5$.