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MATH / Kite ABCD (a quadrilateral with two pairs of adjacent equal sides) has coordinates A (0,7), B (1,0), C (12,−2), and D (7,8). What is the area of ABCD, given that the area of a kite…

Problem

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problem

Kite ABCDABCD (a quadrilateral with two pairs of adjacent equal sides) has coordinates A(0,7),B(1,0),C(12,−2),A\ (0,7),\ B\ (1,0),\ C\ (12,-2), and D(7,8).D\ (7,8). What is the area of ABCD,ABCD, given that the area of a kite is equal to half the product of its diagonals? [asy] string sp(pair P, string P2){return "$" + P2 + "\,(" + string(P.x) + "," + string(P.y) + ")$";} size(150); defaultpen(fontsize(10)); draw((-5,0)--(15,0),Arrows(4)); draw((0,-5)--(0,10),Arrows(4)); pair A=(0,7),B=(1,0),C=(12,-2),D=(7,8); draw(A--B--C--D--cycle, linewidth(0.7)); draw(A--C, dashed); draw(B--D, dashed); label(sp(A,"A"),A,W); label(sp(B,"B"),B,S); label(sp(C,"C"),C,E); label(sp(D,"D"),D,N); [/asy]
Plain-text mathematical notation (without MathML)
Kite ABCD (a quadrilateral with two pairs of adjacent equal sides) has coordinates A (0,7), B (1,0), C (12,−2), and D (7,8). What is the area of ABCD, given that the area of a kite is equal to half the product of its diagonals?

[asy]
string sp(pair P, string P2){return "$" + P2 + "\,(" + string(P.x) + "," + string(P.y) + ")$";}
size(150); defaultpen(fontsize(10)); draw((-5,0)--(15,0),Arrows(4)); draw((0,-5)--(0,10),Arrows(4)); pair A=(0,7),B=(1,0),C=(12,-2),D=(7,8); draw(A--B--C--D--cycle, linewidth(0.7)); draw(A--C, dashed); draw(B--D, dashed); label(sp(A,"A"),A,W); label(sp(B,"B"),B,S); label(sp(C,"C"),C,E); label(sp(D,"D"),D,N);
[/asy]
Original LaTeX notation
Kite $ABCD$ (a quadrilateral with two pairs of adjacent equal sides) has coordinates $A\ (0,7),\ B\ (1,0),\ C\ (12,-2),$ and $D\ (7,8).$ What is the area of $ABCD,$ given that the area of a kite is equal to half the product of its diagonals?

[asy]
string sp(pair P, string P2){return "$" + P2 + "\,(" + string(P.x) + "," + string(P.y) + ")$";}
size(150); defaultpen(fontsize(10)); draw((-5,0)--(15,0),Arrows(4)); draw((0,-5)--(0,10),Arrows(4)); pair A=(0,7),B=(1,0),C=(12,-2),D=(7,8); draw(A--B--C--D--cycle, linewidth(0.7)); draw(A--C, dashed); draw(B--D, dashed); label(sp(A,"A"),A,W); label(sp(B,"B"),B,S); label(sp(C,"C"),C,E); label(sp(D,"D"),D,N);
[/asy]

level

Level 3

type

Algebra

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Source and history

task_id
a3905f9a-900c-556d-b81e-0118c299cd6f
task_key
algebra--test--a3905f9a-900c-556d-b81e-0118c299cd6f
task_revision_id
3
config / split
algebra / test

Official source

initial import