Therefore, the Midpoint Formula did indeed return the midpoint between the two given points. Find the radius of a circle with a diameter whose endpoints are, Find the length of the diameter with endpoints, Solve for the radius by dividing the diameter by, The blue dots are the endpoints of diameter and the green dot is the center of the circle (calculated using the, the second x-coordinate subtracted by the first x-coordinate, the second y-coordinate subtracted by the first y-coordinate. The distance formula is nicely versatile. First, I'll find the midpoint according to the Formula: ([-3+5]/2, [-2+6]/2) = (2/2, 4/2) = (1, 2). The only true failure is not trying at all. Then substitute the values into the formula and solve. The very essence of the Distance Formula is to calculate the length of the hypotenuse of the right triangle which is represented by the letter c. That’s why we can claim that the idea of the Distance Formula is borrowed and derived from the Pythagorean Theorem. Notice that one point, namely \left( {x, - \,4} \right), contains the variable \large\color{red}x instead of a specific number. Interactive Graph - Distance Formula Remember that x-coordinate is always the first value of the ordered pair \left( {{\color{red}{x}},y} \right). Formula Examples. ), URL:, © 2020 Purplemath. I suggest that you approach this just the same as the previous problems. Then draw the vertical line through x = 4. You also don't want to be careless with the squaring inside the Formula. If you get in the habit of omitting the square root and then "remembering" to put it back in when you check your answers in the back of the book, then you'll forget the square root on the test, and you'll miss easy points. Remember that you simplify inside the parentheses before you square, not after (due to the Order of Operations), and remember that the square is on everything inside the parentheses, including the minus sign (if your subtraction results in a negative number); the square of a negative is always a positive. Be careful you don't subtract an x from a y, or vice versa; make sure you've paired the numbers properly. How far is the point (6,8) from the origin? The Distance Formula. Purplemath. Watch the video on distance formula by Khan Academy We use cookies to give you the best experience on our website. Consequently, the second point would be \left( {6,8} \right). Please accept "preferences" cookies in order to enable this widget. If you're not sure which format is preferred, do both, like this: katex.render("d = \\sqrt{53\\,} \\approx 7.28", dist10); Very often you will encounter the Distance Formula in veiled forms. What is the distance between the points (–1, –1) and (4, –5)? It's okay not to know! Find the distance between the two points (–3, 2) and (3, 5). Otherwise, check your browser settings to turn cookies off or discontinue using the site. We explain Distance Formula in the Real World with video tutorials and quizzes, using our Many Ways(TM) approach from multiple teachers. Also, my two distances are the same. Be careful you don't subtract an x from a y, or vice versa; make sure you've paired the numbers properly. You might be surprised how often you can figure stuff out, if only you give yourself permission to be confused at the start. We substitute the values above into the Distance Formula below then simplify. You can use the Mathway widget below to practice finding the distance between two points. If that’s the case, then the radius is half the length of the diameter. That's okay; try something else. First, I'll find the distance of the point (–3, –2) from (1, 2): d1 = √[(-3 - 1)2 + (-2 - 2)2] = √[(-4)2 + (-4)2] = √[16 + 16] = √[32] = √[16×2] = 4 √[2]. If we assign \left( { - 1, - 1} \right) as our first point then, In the same manner, assigning \left( {4, - 5} \right) as our second point, we have. In this case, you will see immediately that you won’t get a value as the distance. How many units apart are the points (–4, –3) and (4, 3)? Sometimes you may wonder if switching the points in calculating the distance can affect the final outcome. The Distance Formula is a useful tool in finding the distance between two points which can be arbitrarily represented as points \left( {{x_1},{y_1}} \right) and \left( {{x_2},{y_2}} \right).. Distance, speed and time formulae. Distance Formula in Coordinate Geometry To locate the position of an object or a point in a plane, we do it with the help of coordinate geometry. The Distance Formula itself is actually derived from the Pythagorean Theorem which is {a^2} + {b^2} = {c^2} where c is the longest side of a right triangle (also known as the hypotenuse) and a and b are the other shorter sides (known as the legs of a right triangle).