Geometry

Distance Formula

100

Find AB given A(-4, 1) and B(3, -1).

sqrt(53)

200

Find XY given X(-5, 3) and Y(-2, -3).

sqrt(45)

300

Find EF given E(-7, -2) and F(11, 3).

sqrt(349)

400

Find GH given G(0, -3) and H(-9, -7).

sqrt(97)

500

Find JK given J(3, -5) and K(-8, 0).

sqrt(146)

Midpoints

100

Find the midpoint of GH given G(7, -5) and H(9, -1).

(8, -3)

200

Find the midpoint of AB given A(-7, 4) and B(3, -4).

(-2, 0)

300

Find the midpoint of ST given S(–8, –6) and T(–14, –20).

(-11, -13)

400

If P is the midpoint of XY, XP = 8x - 2, and PY = 12x - 30, find the value of x.

7

500

If G is the midpoint of FH, FG = 14x + 25, and GH = 73 - 2x, find FH.

134

Finding Missing Endpoints

100

Find the coordinates of A if M(-1, 2) is the midpoint of AB and B has coordinates of (3, -5).

(-5, 9)

200

Find the coordinates of J if K(-5, 10) is the midpoint of JL and L has coordinates of (-8, 6).

(-2, 14)

300

Find the coordinates of R if Q(-1, 3) is the midpoint of PR and P has coordinates of (5, 6).

(-7, 0)

400

Find the coordinates of S if M(7.5, 8.5) is the midpoint of ST and T has coordinates of (6, 6).

(9, 11)

500

Find the coordinates of G if M(–4.5, –40) is the midpoint of GH and H has coordinates of (–17, 8).

(8, -88)

Partitioning Line Segments

100

Given line segment DF with D(-1, 11) and F(-9, -5). If E partitions DF such that the ratio of DE to DF is 5:8, find the coordinates of E.

E(-6, 1)

200

Given line segment AC with A(3, 4) and C(-9, -2). If B partitions AC such that the ratio of AB to BC is 1:5, find the coordinates of B.

B(1, 3)

300

Given line segment WY with W(3, 7) and Y(13, -8). If X partitions WY such that the ratio of WX to XY is 3:2, find the coordinates of X.

X(9, -2)

400

Given line segment XZ with X(-4, 3) and Z(6, -2), find the coordinates of Y if Y divides XZ one-fifth of the way from X to Z.

Y(-2, 2)

500

Given line segment JL with J(8, -8) and L(-16, -2), find the coordinates of K if K divides JL two-thirds of the way from J to L.

K(-8, -4)