Question

Find x if distance between points L(x,7) and M(1, 15 is 10 ?​

Answer 1

Answer:

refer to this image hope it will help you

Answer 2

Distance formula:-

$\boxed{\sf \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}}$

$\\ \sf\longmapsto \sqrt{ {(1 - x) }^{2} + ( {15 - 7)}^{2} } = 10 \\ \\ \sf\longmapsto \sqrt{1 - 2x + {x}^{2} + {8}^{2} } = 10 \\ \\ \sf\longmapsto \sqrt{1 - 2x + {x}^{2} + 64} = 10 \\ \\ \sf\longmapsto \sqrt{ {x}^{2} - 2x = 65} = 10 \\ \\ \sf\longmapsto {x}^{2} - 2x + 65 = 10 {}^{2} \\ \\ \sf\longmapsto {x}^{2} - 2x + 65 = 100 \\ \\ \sf\longmapsto {x}^{2} - 2x = 100 - 65 \\ \\ \sf\longmapsto {x}^{2} - 2x = 35 \\ \\ \sf\longmapsto {x}^{2} - 2x - 35 = 0 \\ \\ \sf\longmapsto {x}^{2} + 5x - 7x + 35 = 0 \\ \\ \sf\longmapsto x(x + 5) - 7(x + 5) = 0 \\ \\ \sf\longmapsto (x + 5)(x - 7 )= 0 \\ \\ \sf\longmapsto (x + 5) = 0 \: or \: (x - 7) = 0 \\ \\ \sf\longmapsto x = - 5 \:or \: x = 7$