Midpoint Formula

Front

What is the Midpoint Formula?

Back

The Midpoint Formula is used to find the midpoint (M) between two points (x1, y1) and (x2, y2) in a coordinate plane. It is given by: M = \left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right).

Tags

CCSS.HSG.GPE.B.6

Front

Find the midpoint of the points (2, 3) and (4, 7).

Back

M = \left(\frac{2 + 4}{2}, \frac{3 + 7}{2}\right) = (3, 5).

Tags

CCSS.HSG.GPE.B.6

Front

What is the significance of the midpoint in geometry?

Back

The midpoint divides a line segment into two equal parts, making it a crucial concept in geometry for bisecting segments.

Tags

CCSS.HSG.GPE.B.6

Front

Calculate the midpoint of (-8, 6) and (5, -7).

Back

M = \left(\frac{-8 + 5}{2}, \frac{6 - 7}{2}\right) = \left(-\frac{3}{2}, -\frac{1}{2}\right).

Tags

CCSS.HSG.GPE.B.6

Front

What is the midpoint of the segment with endpoints (4, 12) and (-6, 14)?

Back

M = \left(\frac{4 + (-6)}{2}, \frac{12 + 14}{2}\right) = (-1, 13).

Tags

CCSS.HSG.GPE.B.6

Front

Find the midpoint of the points (3, -1) and (7, -5).

Back

M = \left(\frac{3 + 7}{2}, \frac{-1 + (-5)}{2}\right) = (5, -3).

Tags

CCSS.HSG.GPE.B.6

Front

What is the midpoint of the points (-1, 9) and (7, -1)?

Back

M = \left(\frac{-1 + 7}{2}, \frac{9 + (-1)}{2}\right) = (3, 4).

Tags

CCSS.HSG.GPE.B.6

Front

If the midpoint is (5, -2) and one endpoint is (3, -1), what is the other endpoint?

Back

Let the other endpoint be (x, y). Then, M = \left(\frac{3 + x}{2}, \frac{-1 + y}{2}\right) = (5, -2). Solving gives x = 7 and y = -5.

Tags

CCSS.HSG.GPE.B.6

Front

What is the formula to find the x-coordinate of the midpoint?

Back

The x-coordinate of the midpoint is given by: \frac{x_1 + x_2}{2}.

Tags

CCSS.HSG.GPE.B.6

Front

What is the formula to find the y-coordinate of the midpoint?

Back

The y-coordinate of the midpoint is given by: \frac{y_1 + y_2}{2}.

Tags

CCSS.HSG.GPE.B.6