Coordinates to Find Perimeter and Area - Geometry
Card 1 of 30
Find the distance between $(2,1)$ and $(6,1)$.
Find the distance between $(2,1)$ and $(6,1)$.
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$4$. Horizontal distance: $|6-2|=4$
$4$. Horizontal distance: $|6-2|=4$
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Find the distance between $(0,0)$ and $(3,4)$.
Find the distance between $(0,0)$ and $(3,4)$.
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$5$. $\sqrt{3^2+4^2}=\sqrt{25}=5$
$5$. $\sqrt{3^2+4^2}=\sqrt{25}=5$
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Find the distance between $(-1,-2)$ and $(2,2)$.
Find the distance between $(-1,-2)$ and $(2,2)$.
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$5$. $\sqrt{(2-(-1))^2+(2-(-2))^2}=\sqrt{9+16}=5$
$5$. $\sqrt{(2-(-1))^2+(2-(-2))^2}=\sqrt{9+16}=5$
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Find the distance between $(5,-1)$ and $(5,7)$.
Find the distance between $(5,-1)$ and $(5,7)$.
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$8$. Vertical distance: $|7-(-1)|=8$
$8$. Vertical distance: $|7-(-1)|=8$
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Find the area of the rectangle with vertices $(0,0)$, $(2,0)$, $(2,2)$, $(0,2)$.
Find the area of the rectangle with vertices $(0,0)$, $(2,0)$, $(2,2)$, $(0,2)$.
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$4$. Square with side length $2$: area is $2^2=4$.
$4$. Square with side length $2$: area is $2^2=4$.
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Find the area of the triangle with vertices $(0,0)$, $(3,0)$, $(0,4)$.
Find the area of the triangle with vertices $(0,0)$, $(3,0)$, $(0,4)$.
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$6$. Right triangle: $\frac{1}{2} \times 3 \times 4 = 6$
$6$. Right triangle: $\frac{1}{2} \times 3 \times 4 = 6$
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Find the area of the axis-aligned rectangle with corners $(1,2)$ and $(6,7)$.
Find the area of the axis-aligned rectangle with corners $(1,2)$ and $(6,7)$.
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$25$. Width $5$, height $5$: area is $25$.
$25$. Width $5$, height $5$: area is $25$.
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What is the area formula for a triangle with base $b$ and height $h$?
What is the area formula for a triangle with base $b$ and height $h$?
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$A=\frac{1}{2}bh$. Triangle area is half the base times height.
$A=\frac{1}{2}bh$. Triangle area is half the base times height.
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What is the perimeter formula for a rectangle with side lengths $\ell$ and $w$?
What is the perimeter formula for a rectangle with side lengths $\ell$ and $w$?
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$P=2\ell+2w$. Sum of all four sides: two lengths plus two widths.
$P=2\ell+2w$. Sum of all four sides: two lengths plus two widths.
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What is the area formula for a rectangle with side lengths $\ell$ and $w$?
What is the area formula for a rectangle with side lengths $\ell$ and $w$?
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$A=\ell w$. Standard rectangle area formula: length times width.
$A=\ell w$. Standard rectangle area formula: length times width.
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What is the perimeter of a polygon in the coordinate plane in terms of side lengths?
What is the perimeter of a polygon in the coordinate plane in terms of side lengths?
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Sum of all side lengths (use $d$ for each side). Apply distance formula to each consecutive pair of vertices.
Sum of all side lengths (use $d$ for each side). Apply distance formula to each consecutive pair of vertices.
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What is the vertical distance between $(x,y_1)$ and $(x,y_2)$?
What is the vertical distance between $(x,y_1)$ and $(x,y_2)$?
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$|y_2-y_1|$. Vertical distance when $x$-coordinates are equal.
$|y_2-y_1|$. Vertical distance when $x$-coordinates are equal.
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What is the horizontal distance between $(x_1,y)$ and $(x_2,y)$?
What is the horizontal distance between $(x_1,y)$ and $(x_2,y)$?
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$|x_2-x_1|$. Horizontal distance when $y$-coordinates are equal.
$|x_2-x_1|$. Horizontal distance when $y$-coordinates are equal.
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Find the perimeter of the triangle with vertices $(0,0)$, $(6,0)$, $(0,8)$.
Find the perimeter of the triangle with vertices $(0,0)$, $(6,0)$, $(0,8)$.
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$24$. Sides: $6+8+10=24$ using distance formula.
$24$. Sides: $6+8+10=24$ using distance formula.
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Find the area of the axis-aligned rectangle with corners $(0,0)$ and $(6,8)$.
Find the area of the axis-aligned rectangle with corners $(0,0)$ and $(6,8)$.
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$48$. Width $6$, height $8$: area is $6 \times 8=48$.
$48$. Width $6$, height $8$: area is $6 \times 8=48$.
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Find the perimeter of the axis-aligned rectangle with corners $(0,0)$ and $(6,8)$.
Find the perimeter of the axis-aligned rectangle with corners $(0,0)$ and $(6,8)$.
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$28$. Width $6$, height $8$: perimeter is $2(6+8)=28$.
$28$. Width $6$, height $8$: perimeter is $2(6+8)=28$.
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Find the length of a rectangle diagonal with corners $(0,0)$ and $(6,8)$.
Find the length of a rectangle diagonal with corners $(0,0)$ and $(6,8)$.
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$10$. Diagonal distance: $\sqrt{6^2+8^2}=\sqrt{100}=10$
$10$. Diagonal distance: $\sqrt{6^2+8^2}=\sqrt{100}=10$
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Identify whether lines through $(0,0)$ to $(2,2)$ and $(1,0)$ to $(3,2)$ are parallel.
Identify whether lines through $(0,0)$ to $(2,2)$ and $(1,0)$ to $(3,2)$ are parallel.
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Yes, both slopes are $1$. Both segments have slope $1$, so they're parallel.
Yes, both slopes are $1$. Both segments have slope $1$, so they're parallel.
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Identify whether segments with slopes $\frac{2}{3}$ and $-\frac{3}{2}$ are perpendicular.
Identify whether segments with slopes $\frac{2}{3}$ and $-\frac{3}{2}$ are perpendicular.
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Yes, because $\frac{2}{3}\cdot\left(-\frac{3}{2}\right)=-1$. Product of slopes equals $-1$, confirming perpendicularity.
Yes, because $\frac{2}{3}\cdot\left(-\frac{3}{2}\right)=-1$. Product of slopes equals $-1$, confirming perpendicularity.
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Find the area of the triangle with vertices $(0,0)$, $(4,0)$, $(4,3)$.
Find the area of the triangle with vertices $(0,0)$, $(4,0)$, $(4,3)$.
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$6$. Right triangle: $\frac{1}{2} \times 4 \times 3 = 6$
$6$. Right triangle: $\frac{1}{2} \times 4 \times 3 = 6$
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Find the perimeter of the triangle with vertices $(0,0)$, $(4,0)$, $(4,3)$.
Find the perimeter of the triangle with vertices $(0,0)$, $(4,0)$, $(4,3)$.
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$12$. Sides: $4+3+5=12$ using distance formula.
$12$. Sides: $4+3+5=12$ using distance formula.
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Find the distance between $(3,4)$ and $(7,1)$.
Find the distance between $(3,4)$ and $(7,1)$.
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$5$. $\sqrt{(7-3)^2+(1-4)^2}=\sqrt{16+9}=5$
$5$. $\sqrt{(7-3)^2+(1-4)^2}=\sqrt{16+9}=5$
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Find the distance between $(-1,-2)$ and $(2,2)$.
Find the distance between $(-1,-2)$ and $(2,2)$.
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$5$. $\sqrt{(2-(-1))^2+(2-(-2))^2}=\sqrt{9+16}=5$
$5$. $\sqrt{(2-(-1))^2+(2-(-2))^2}=\sqrt{9+16}=5$
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Find the distance between $(1,1)$ and $(4,5)$.
Find the distance between $(1,1)$ and $(4,5)$.
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$5$. $\sqrt{(4-1)^2+(5-1)^2}=\sqrt{9+16}=5$
$5$. $\sqrt{(4-1)^2+(5-1)^2}=\sqrt{9+16}=5$
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Find the area of the triangle with vertices $(0,0)$, $(2,0)$, $(0,2)$.
Find the area of the triangle with vertices $(0,0)$, $(2,0)$, $(0,2)$.
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$2$. Right triangle: $\frac{1}{2} \times 2 \times 2 = 2$
$2$. Right triangle: $\frac{1}{2} \times 2 \times 2 = 2$
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Find the perimeter of the triangle with vertices $(0,0)$, $(2,0)$, $(0,2)$.
Find the perimeter of the triangle with vertices $(0,0)$, $(2,0)$, $(0,2)$.
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$4+2\sqrt{2}$. Sides: $2+2+2\sqrt{2}=4+2\sqrt{2}$
$4+2\sqrt{2}$. Sides: $2+2+2\sqrt{2}=4+2\sqrt{2}$
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Find the area of the rectangle with vertices $(0,0)$, $(2,0)$, $(2,2)$, $(0,2)$.
Find the area of the rectangle with vertices $(0,0)$, $(2,0)$, $(2,2)$, $(0,2)$.
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$4$. Square with side length $2$: area is $2^2=4$.
$4$. Square with side length $2$: area is $2^2=4$.
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Find the perimeter of the polygon with vertices $(0,0)$, $(2,0)$, $(2,2)$, $(0,2)$.
Find the perimeter of the polygon with vertices $(0,0)$, $(2,0)$, $(2,2)$, $(0,2)$.
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$8$. Square with side length $2$: perimeter is $4 \times 2=8$.
$8$. Square with side length $2$: perimeter is $4 \times 2=8$.
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Find the perimeter of the axis-aligned rectangle with corners $(-3,-1)$ and $(2,4)$.
Find the perimeter of the axis-aligned rectangle with corners $(-3,-1)$ and $(2,4)$.
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$20$. Width $5$, height $5$: perimeter is $2(5+5)=20$.
$20$. Width $5$, height $5$: perimeter is $2(5+5)=20$.
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Find the area of the axis-aligned rectangle with corners $(-3,-1)$ and $(2,4)$.
Find the area of the axis-aligned rectangle with corners $(-3,-1)$ and $(2,4)$.
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$25$. Width $5$, height $5$: area is $25$.
$25$. Width $5$, height $5$: area is $25$.
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