Question

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A landscaper is putting a border on each side of a triangular garden . She plots the vertices of the garden and on a coordinate grid . (- 2, 3), (5, 5) (7, - 3) Which expression can be used to find the length of the side of the triangle represented by the vertices ( 5,5 ) and the graph ?

Answer 1

Answer:

The expression that can be used to find the length of the side of the triangle represented by the vertices (5, 5), and (7, -3) is given as follows;

A. $\sqrt{\left (5-7 \right )^{2}+\left (5-(-3) \right )^{2}}$

Step-by-step explanation:

The formula for finding the length, 'l', of a line given the (x, y) coordinates is presented as follows;

$l = \sqrt{\left (y_{2}-y_{1} \right )^{2}+\left (x_{2}-x_{1} \right )^{2}}$

The given coordinates of the vertices of the triangular garden are;

(-2, 3), (5, 5), and (7, -3)

Therefore, the length of the side of the triangle that is represented by the vertices (5, 5) and (7, -3) is found by substituting the 'x', and 'y', values as follows;

$l_{(Side \, of \, the \, triangle)} = \sqrt{\left (5-7 \right )^{2}+\left (5-(-3) \right )^{2}}$

Which can be further simplified as follows;

$\sqrt{\left (5-7 \right )^{2}+\left (5-(-3) \right )^{2}} = \sqrt{\left (-2 \right )^{2}+\left (8 \right )^{2}} = \sqrt{68} = 2 \cdot \sqrt{17}$