Question 10 of 26
What is the distance between the points \( (4,10) \) and \( (-3,-14) \) on the coordinate plane?
A. 10 units
B. 50 units
C. 25 units
D. 5 units

Answer

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Answer

Apply the distance formula: \(d = \sqrt{(\Delta x^{2} + \Delta y^{2})} = \sqrt{49 + 576} = \sqrt{625} = 25\sqrt{2}\)

Steps

Step 1 ：Determine the differences in \(x\) and \(y\) coordinates: \(\Delta x = -3 -4 = -7\), \(\Delta y = -14 - 10 = -24\)

Step 2 ：Calculate the square of differences: \(\Delta x^{2} = (-7)^{2} = 49\), \(\Delta y^{2} = (-24)^{2} = 576\)

Step 3 ：Apply the distance formula: \(d = \sqrt{(\Delta x^{2} + \Delta y^{2})} = \sqrt{49 + 576} = \sqrt{625} = 25\sqrt{2}\)