Question

In the coordinate plane, what is the length of the line segment that connects points (4, 1) and (9, 7)​

Answer 1

$\bf \underline{Given \: points } = \sf (4, 1) \: and \: (9, 7)$

$\bf \underline{ To \: find }$

$\sf Length \: of \: line \: segment \: that \: connect \: these \: points = \: ?$

$\bf \underline{\underline{ Solution }}$

To find the length between any two given points on a line segment in Coordinate plane we have to use distance formula.

$\sf Let \: the \: points \: be, A(4, 1) \: and \: B(9, 7)$

$\bf \underline{ Now},$

$\sf{AB = \sqrt{(x _{2} - x_1)^{2} + (y_2 - y_1)^{2} } }$

$\bf \underline{Where},$

$\sf \implies x_1 = 4$

$\sf \implies x_2 = 9$

$\sf \implies y_1 = 1$

$\sf \implies y_2 = 7$

$\sf Substituting \: the \: values,$

$\sf{AB = \sqrt{(9 - 4)^{2} + (7 - 1)^{2} } }$

$\sf{AB = \sqrt{(5)^{2} + ( 6)^{2} } }$

$\sf{AB = \sqrt{(5 \times 5) + (6 \times 6) } }$

$\sf{AB = \sqrt{25 + 36 } }$

$\sf{AB = \sqrt{61 } \: units }$

$\bf \underline{Therefore},$

The length of line segment that connects the points (4, 1) and (9, 7) is √61 units.