Question

which triangle would be most helpful in finding the distance between the points $(-4,3)$ and $(1,-2)$ on the coordinate plane?

Explanation:

Step1: Determine the horizontal and vertical distances

The horizontal distance between \(x\) - coordinates \(-4\) and \(1\) is \(|1-(-4)| = 5\). The vertical distance between \(y\) - coordinates \(3\) and \(-2\) is \(| - 2 - 3|=5\). We need a right - triangle where the legs are parallel to the \(x\) - axis and \(y\) - axis.

Step2: Analyze each option

• Option1: The dashed lines (legs of the supposed right - triangle) are not parallel to the axes.
• Option2: The vertical dashed line has a length of \(|3 - (-2)| = 5\) (vertical distance between \(y\) values) and the horizontal dashed line has a length of \(|1-(-4)|=5\) (horizontal distance between \(x\) values). The legs of the right - triangle (dashed lines) are parallel to the \(x\) - axis and \(y\) - axis.
• Option3: The dashed lines (legs of the supposed right - triangle) are not parallel to the axes.
• Option4: The dashed lines (legs of the supposed right - triangle) are not parallel to the axes.

Answer:

The second triangle (the one in the top - right of the four options) is most helpful.